%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU672^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:06 AM UTC 2026
% Result : Theorem 76.61s 12.46s
% Output : Refutation 76.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 27
% Syntax : Number of formulae : 137 ( 47 unt; 0 typ; 12 def)
% Number of atoms : 3651 ( 928 equ; 21 cnn)
% Maximal formula atoms : 192 ( 26 avg)
% Number of connectives : 2319 ( 79 ~; 90 |; 608 &; 660 @)
% ( 12 <=>; 825 =>; 0 <=; 0 <~>)
% Maximal formula depth : 203 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 248 ( 241 usr; 211 con; 0-3 aty)
% ( 31 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 222 ( 138 ^; 68 !; 16 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $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_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_242,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_243,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_249,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f8478,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1531,f1536,f1654,f1668,f3763,f3785,f3802,f3841,f3870,f4186,f8447,f8453,f8470]) ).
thf(f8470,plain,
~ spl6_229,
inference(avatar_contradiction_clause,[status(thm)],[f8469]) ).
thf(f8469,plain,
( $false
| ~ spl6_229 ),
inference(trivial_inequality_removal,[status(thm)],[f8468]) ).
thf(f8468,plain,
( ( $true = $false )
| ~ spl6_229 ),
inference(duplicate_literal_removal,[status(thm)],[f8461]) ).
thf(f8461,plain,
( ( $true = $false )
| ( $true = $false )
| ~ spl6_229 ),
inference(superposition,[status(thm)],[f599,f8452]) ).
thf(f8452,plain,
( ( ( $true
& $false )
= $true )
| ~ spl6_229 ),
inference(avatar_component_clause,[status(thm)],[f8450]) ).
thf(f8450,definition,
( spl6_229
<=> ( ( $true
& $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_229])],[avatar_definition]) ).
thf(f599,plain,
! [X2: $o,X1: $o] :
( ( ( X1
& X2 )
= $false )
| ( $true = X2 ) ),
introduced(definition,[],[logical_and_proxy_axiom]) ).
thf(f8453,plain,
( spl6_229
| ~ spl6_90 ),
inference(avatar_split_clause,[status(thm)],[f8448,f4183,f8450]) ).
thf(f4183,definition,
( spl6_90
<=> ( $true
= ( ( subset @ sK3 @ ( cartprod @ sK2 @ sK4 ) )
& $false ) ) ),
introduced(definition,[new_symbols(naming,[spl6_90])],[avatar_definition]) ).
thf(f8448,plain,
( ( ( $true
& $false )
= $true )
| ~ spl6_90 ),
inference(forward_demodulation,[status(thm)],[f4185,f4175]) ).
thf(f4175,plain,
( $true
= ( subset @ sK3 @ ( cartprod @ sK2 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f4168]) ).
thf(f4168,plain,
( ( $true
= ( subset @ sK3 @ ( cartprod @ sK2 @ sK4 ) ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f1215,f598]) ).
thf(f598,plain,
! [X2: $o,X1: $o] :
( ( ( X1
& X2 )
= $false )
| ( $true = X1 ) ),
introduced(definition,[],[logical_and_proxy_axiom]) ).
thf(f1215,plain,
( ( ( subset @ sK3 @ ( cartprod @ sK2 @ sK4 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK3 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK3 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1072]) ).
thf(f1072,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
@ sK2
@ sK4
@ sK3 ) ),
inference(definition_unfolding,[status(thm)],[f757,f1004]) ).
thf(f1004,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f636,f901,f1002]) ).
thf(f1002,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f653,f894]) ).
thf(f894,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f243]) ).
thf(f243,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f242]) ).
thf(f242,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f156]) ).
thf(f156,axiom,
( singleton
= ( ^ [X3: $i] :
? [X1: $i] :
( ( in @ X1 @ X3 )
& ( ( setadjoin @ X1 @ emptyset )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',singleton) ).
thf(f653,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f353]) ).
thf(f353,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f352]) ).
thf(f352,plain,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
inference(rectify,[status(thm)],[f158]) ).
thf(f158,axiom,
( ( ^ [X3: $i,X0: $i > $o] :
( singleton
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) )
= ex1 ),
file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',ex1) ).
thf(f901,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f233]) ).
thf(f233,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f232]) ).
thf(f232,plain,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f186]) ).
thf(f186,axiom,
( breln
= ( ^ [X3: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',breln) ).
thf(f636,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f425]) ).
thf(f425,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f424]) ).
thf(f424,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) )
= func ),
inference(rectify,[status(thm)],[f194]) ).
thf(f194,axiom,
( ( ^ [X3: $i,X4: $i,X12: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( in @ ( kpair @ X1 @ X2 ) @ X12 ) ) )
& ( breln @ X3 @ X4 @ X12 ) ) )
= func ),
file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',func) ).
thf(f757,plain,
( $true
= ( func @ sK2 @ sK4 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f608]) ).
thf(f608,plain,
( ( disjointsetsI1 = $true )
& ( symdiffIneg1 = $true )
& ( quantDeMorgan4 = $true )
& ( setminusERneg = $true )
& ( dpsetconstrI = $true )
& ( dsetconstr__Cong = $true )
& ( cartprodmempair = $true )
& ( binintersectI = $true )
& ( setukpairinjL1 = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( eqimpsubset1 = $true )
& ( setoftrueEq = $true )
& ( setminusSubset1 = $true )
& ( emptysetsubset = $true )
& ( setadjoinSub2 = $true )
& ( subset2powerset = $true )
& ( setadjoinSub = $true )
& ( exuE2 = $true )
& ( emptyinPowerset = $true )
& ( setukpairIL = $true )
& ( setminusILneg = $true )
& ( setadjoinIR = $true )
& ( binintersectSubset4 = $true )
& ( setminusEL = $true )
& ( eqinunit = $true )
& ( kpairsurjEq = $true )
& ( noeltsimpempty = $true )
& ( subsetE2 = $true )
& ( dpsetconstrSub = $true )
& ( descr__Cong = $true )
& ( sepSubset = $true )
& ( upairequniteq = $true )
& ( setunionE = $true )
& ( cartprodfstpairEq = $true )
& ( dpsetconstrEL2 = $true )
& ( kpairiskpair = $true )
& ( singletonsubset = $true )
& ( exuE1 = $true )
& ( setadjoinAx = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( powersetAx = $true )
& ( subsetE = $true )
& ( ubforcartprodlem1 = $true )
& ( cartprodmempair1 = $true )
& ( eqimpsubset2 = $true )
& ( upairsetIR = $true )
& ( setunionE2 = $true )
& ( cartprodsndpairEq = $true )
& ( theprop = $true )
& ( binintersectSubset1 = $true )
& ( powersetI = $true )
& ( setminusER = $true )
& ( dpsetconstrEL1 = $true )
& ( exuE3u = $true )
& ( powersetsubset = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( setukpairinjR12 = $true )
& ( setminusSubset2 = $true )
& ( upairinpowunion = $true )
& ( setukpairinjR11 = $true )
& ( binunionE = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan3 = $true )
& ( prop2set2propI = $true )
& ( exuI1 = $true )
& ( ex1I2 = $true )
& ( upairsetIL = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyInPowerset = $true )
& ( setunion__Cong = $true )
& ( vacuousDall = $true )
& ( subsetRefl = $true )
& ( omegaSAx = $true )
& ( setukpairIR = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrER = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyE1 = $true )
& ( ex1I = $true )
& ( dpsetconstrERa = $true )
& ( setunionsingleton2 = $true )
& ( descrp = $true )
& ( binintersectLsub = $true )
& ( quantDeMorgan2 = $true )
& ( setOfPairsIsBReln = $true )
& ( symdiffI2 = $true )
& ( binunionEcases = $true )
& ( notdexE = $true )
& ( secondinupair = $true )
& ( ksndpairEq = $true )
& ( ubforcartprodlem2 = $true )
& ( kfstsingleton = $true )
& ( bs114d = $true )
& ( cartprodfstin = $true )
& ( setadjoinIL = $true )
& ( setukpairinjR2 = $true )
& ( notdallE = $true )
& ( notinsingleton = $true )
& ( binintersectSubset2 = $true )
& ( upairset2IR = $true )
& ( setminusLsub = $true )
& ( setextAx = $true )
& ( emptysetE = $true )
& ( setadjoinE = $true )
& ( binunionRsub = $true )
& ( subPowSU = $true )
& ( setunionAx = $true )
& ( nonemptyImpWitness = $true )
& ( binunionLsub = $true )
& ( cartprodpairmemEL = $true )
& ( emptysetimpfalse = $true )
& ( wellorderingAx = $true )
& ( exuI2 = $true )
& ( subsetemptysetimpeq = $true )
& ( powersetE1 = $true )
& ( setextsub = $true )
& ( setukpairinjL = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( binintersectSubset3 = $true )
& ( binunionIL = $true )
& ( nonemptyI = $true )
& ( setminusELneg = $true )
& ( upairset2E = $true )
& ( powersetE = $true )
& ( binintersectER = $true )
& ( ex1E1 = $true )
& ( prop2setI = $true )
& ( exuEu = $true )
& ( upairsubunion = $true )
& ( exuE3e = $true )
& ( $true
= ( func @ sK2 @ sK4 @ sK3 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( in @ ( kpair @ sK5 @ Y0 ) @ sK3 ) ) ) )
& ( ( in @ sK5 @ sK2 )
= $true )
& ( subsetTrans = $true )
& ( nonemptyI1 = $true )
& ( powerset__Cong = $true )
& ( setunionI = $true )
& ( kfstpairEq = $true )
& ( singletoninpowerset = $true )
& ( setadjoinOr = $true )
& ( emptyinunitempty = $true )
& ( notsubsetI = $true )
& ( upairsetE = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true )
& ( subsetI1 = $true )
& ( binintersectEL = $true )
& ( omega0Ax = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( inCongP = $true )
& ( exuI3 = $true )
& ( symdiffI1 = $true )
& ( singletonprop = $true )
& ( notinemptyset = $true )
& ( quantDeMorgan1 = $true )
& ( symdiffE = $true )
& ( setukpairinjR1 = $true )
& ( notequalI1 = $true )
& ( setukpairinjR = $true )
& ( kpairp = $true )
& ( omegaIndAx = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( cartprodpairin = $true )
& ( exu__Cong = $true )
& ( prop2setE = $true )
& ( binintersectRsub = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjL2 = $true )
& ( ksndsingleton = $true )
& ( setminusIRneg = $true )
& ( singletoninpowunion = $true )
& ( binunionIR = $true )
& ( singletonsswitch = $true )
& ( singletonsuniq = $true )
& ( symdiffIneg2 = $true )
& ( setunionsingleton = $true )
& ( cartprodsndin = $true )
& ( setext = $true )
& ( omega__Cong = $true )
& ( dsetconstrI = $true )
& ( powersetI1 = $true )
& ( cartprodpairmemER = $true )
& ( setminusI = $true )
& ( subsetI2 = $true )
& ( setunionsingleton1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f605,f607,f606]) ).
thf(f606,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
=> ( ( $true
= ( func @ sK2 @ sK4 @ sK3 ) )
& ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ sK3 ) ) ) )
& ( $true
= ( in @ X3 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f607,plain,
( ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ sK3 ) ) ) )
& ( $true
= ( in @ X3 @ sK2 ) ) )
=> ( ( $true
!= ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( in @ ( kpair @ sK5 @ Y0 ) @ sK3 ) ) ) )
& ( ( in @ sK5 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f605,plain,
( ( disjointsetsI1 = $true )
& ( symdiffIneg1 = $true )
& ( quantDeMorgan4 = $true )
& ( setminusERneg = $true )
& ( dpsetconstrI = $true )
& ( dsetconstr__Cong = $true )
& ( cartprodmempair = $true )
& ( binintersectI = $true )
& ( setukpairinjL1 = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( eqimpsubset1 = $true )
& ( setoftrueEq = $true )
& ( setminusSubset1 = $true )
& ( emptysetsubset = $true )
& ( setadjoinSub2 = $true )
& ( subset2powerset = $true )
& ( setadjoinSub = $true )
& ( exuE2 = $true )
& ( emptyinPowerset = $true )
& ( setukpairIL = $true )
& ( setminusILneg = $true )
& ( setadjoinIR = $true )
& ( binintersectSubset4 = $true )
& ( setminusEL = $true )
& ( eqinunit = $true )
& ( kpairsurjEq = $true )
& ( noeltsimpempty = $true )
& ( subsetE2 = $true )
& ( dpsetconstrSub = $true )
& ( descr__Cong = $true )
& ( sepSubset = $true )
& ( upairequniteq = $true )
& ( setunionE = $true )
& ( cartprodfstpairEq = $true )
& ( dpsetconstrEL2 = $true )
& ( kpairiskpair = $true )
& ( singletonsubset = $true )
& ( exuE1 = $true )
& ( setadjoinAx = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( powersetAx = $true )
& ( subsetE = $true )
& ( ubforcartprodlem1 = $true )
& ( cartprodmempair1 = $true )
& ( eqimpsubset2 = $true )
& ( upairsetIR = $true )
& ( setunionE2 = $true )
& ( cartprodsndpairEq = $true )
& ( theprop = $true )
& ( binintersectSubset1 = $true )
& ( powersetI = $true )
& ( setminusER = $true )
& ( dpsetconstrEL1 = $true )
& ( exuE3u = $true )
& ( powersetsubset = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( setukpairinjR12 = $true )
& ( setminusSubset2 = $true )
& ( upairinpowunion = $true )
& ( setukpairinjR11 = $true )
& ( binunionE = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan3 = $true )
& ( prop2set2propI = $true )
& ( exuI1 = $true )
& ( ex1I2 = $true )
& ( upairsetIL = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyInPowerset = $true )
& ( setunion__Cong = $true )
& ( vacuousDall = $true )
& ( subsetRefl = $true )
& ( omegaSAx = $true )
& ( setukpairIR = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrER = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyE1 = $true )
& ( ex1I = $true )
& ( dpsetconstrERa = $true )
& ( setunionsingleton2 = $true )
& ( descrp = $true )
& ( binintersectLsub = $true )
& ( quantDeMorgan2 = $true )
& ( setOfPairsIsBReln = $true )
& ( symdiffI2 = $true )
& ( binunionEcases = $true )
& ( notdexE = $true )
& ( secondinupair = $true )
& ( ksndpairEq = $true )
& ( ubforcartprodlem2 = $true )
& ( kfstsingleton = $true )
& ( bs114d = $true )
& ( cartprodfstin = $true )
& ( setadjoinIL = $true )
& ( setukpairinjR2 = $true )
& ( notdallE = $true )
& ( notinsingleton = $true )
& ( binintersectSubset2 = $true )
& ( upairset2IR = $true )
& ( setminusLsub = $true )
& ( setextAx = $true )
& ( emptysetE = $true )
& ( setadjoinE = $true )
& ( binunionRsub = $true )
& ( subPowSU = $true )
& ( setunionAx = $true )
& ( nonemptyImpWitness = $true )
& ( binunionLsub = $true )
& ( cartprodpairmemEL = $true )
& ( emptysetimpfalse = $true )
& ( wellorderingAx = $true )
& ( exuI2 = $true )
& ( subsetemptysetimpeq = $true )
& ( powersetE1 = $true )
& ( setextsub = $true )
& ( setukpairinjL = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( binintersectSubset3 = $true )
& ( binunionIL = $true )
& ( nonemptyI = $true )
& ( setminusELneg = $true )
& ( upairset2E = $true )
& ( powersetE = $true )
& ( binintersectER = $true )
& ( ex1E1 = $true )
& ( prop2setI = $true )
& ( exuEu = $true )
& ( upairsubunion = $true )
& ( exuE3e = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
& ( subsetTrans = $true )
& ( nonemptyI1 = $true )
& ( powerset__Cong = $true )
& ( setunionI = $true )
& ( kfstpairEq = $true )
& ( singletoninpowerset = $true )
& ( setadjoinOr = $true )
& ( emptyinunitempty = $true )
& ( notsubsetI = $true )
& ( upairsetE = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true )
& ( subsetI1 = $true )
& ( binintersectEL = $true )
& ( omega0Ax = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( inCongP = $true )
& ( exuI3 = $true )
& ( symdiffI1 = $true )
& ( singletonprop = $true )
& ( notinemptyset = $true )
& ( quantDeMorgan1 = $true )
& ( symdiffE = $true )
& ( setukpairinjR1 = $true )
& ( notequalI1 = $true )
& ( setukpairinjR = $true )
& ( kpairp = $true )
& ( omegaIndAx = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( cartprodpairin = $true )
& ( exu__Cong = $true )
& ( prop2setE = $true )
& ( binintersectRsub = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjL2 = $true )
& ( ksndsingleton = $true )
& ( setminusIRneg = $true )
& ( singletoninpowunion = $true )
& ( binunionIR = $true )
& ( singletonsswitch = $true )
& ( singletonsuniq = $true )
& ( symdiffIneg2 = $true )
& ( setunionsingleton = $true )
& ( cartprodsndin = $true )
& ( setext = $true )
& ( omega__Cong = $true )
& ( dsetconstrI = $true )
& ( powersetI1 = $true )
& ( cartprodpairmemER = $true )
& ( setminusI = $true )
& ( subsetI2 = $true )
& ( setunionsingleton1 = $true ) ),
inference(flattening,[status(thm)],[f604]) ).
thf(f604,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f249]) ).
thf(f249,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f248]) ).
thf(f248,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X2
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f197]) ).
thf(f197,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ! [X3: $i,X13: $i,X4: $i] :
( ( func @ X3 @ X4 @ X13 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( in @ ( kpair @ X1 @ X2 ) @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f196]) ).
thf(f196,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ! [X3: $i,X13: $i,X4: $i] :
( ( func @ X3 @ X4 @ X13 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( in @ ( kpair @ X1 @ X2 ) @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',funcImageSingleton) ).
thf(f4185,plain,
( ( $true
= ( ( subset @ sK3 @ ( cartprod @ sK2 @ sK4 ) )
& $false ) )
| ~ spl6_90 ),
inference(avatar_component_clause,[status(thm)],[f4183]) ).
thf(f8447,plain,
( ~ spl6_87
| ~ spl6_89 ),
inference(avatar_contradiction_clause,[status(thm)],[f8446]) ).
thf(f8446,plain,
( $false
| ~ spl6_87
| ~ spl6_89 ),
inference(trivial_inequality_removal,[status(thm)],[f8445]) ).
thf(f8445,plain,
( ( $true = $false )
| ~ spl6_87
| ~ spl6_89 ),
inference(forward_demodulation,[status(thm)],[f8444,f3869]) ).
thf(f3869,plain,
( ( $false
= ( $true
=> $false ) )
| ~ spl6_87 ),
inference(avatar_component_clause,[status(thm)],[f3867]) ).
thf(f3867,definition,
( spl6_87
<=> ( $false
= ( $true
=> $false ) ) ),
introduced(definition,[new_symbols(naming,[spl6_87])],[avatar_definition]) ).
thf(f8444,plain,
( ( $true
= ( $true
=> $false ) )
| ~ spl6_89 ),
inference(forward_demodulation,[status(thm)],[f8414,f755]) ).
thf(f755,plain,
( ( in @ sK5 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f608]) ).
thf(f8414,plain,
( ( ( ( in @ sK5 @ sK2 )
=> $false )
= $true )
| ~ spl6_89 ),
inference(superposition,[status(thm)],[f4181,f3726]) ).
thf(f3726,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK3 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3722]) ).
thf(f3722,plain,
( ( $true != $true )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK3 ) ) ) ) ) ) ),
inference(fool_paramodulation,[status(thm)],[f1197]) ).
thf(f1197,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1073]) ).
thf(f1073,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( in @ ( kpair @ sK5 @ Y0 ) @ sK3 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f756,f894]) ).
thf(f756,plain,
( $true
!= ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( in @ ( kpair @ sK5 @ Y0 ) @ sK3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f608]) ).
thf(f4181,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ X0 @ Y1 ) @ sK3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ X0 @ Y1 ) @ sK3 ) ) ) ) ) )
= $true )
| ~ spl6_89 ),
inference(avatar_component_clause,[status(thm)],[f4180]) ).
thf(f4180,definition,
( spl6_89
<=> ! [X0: $i] :
( ( ( in @ X0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ X0 @ Y1 ) @ sK3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ X0 @ Y1 ) @ sK3 ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_89])],[avatar_definition]) ).
thf(f4186,plain,
( spl6_89
| spl6_90 ),
inference(avatar_split_clause,[status(thm)],[f4178,f4183,f4180]) ).
thf(f4178,plain,
! [X0: $i] :
( ( ( ( in @ X0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ X0 @ Y1 ) @ sK3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK4
@ ^ [Y1: $i] : ( in @ ( kpair @ X0 @ Y1 ) @ sK3 ) ) ) ) ) )
= $true )
| ( $true
= ( ( subset @ sK3 @ ( cartprod @ sK2 @ sK4 ) )
& $false ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4165]) ).
thf(f4165,plain,
! [X0: $i] :
( ( $true
= ( ( subset @ sK3 @ ( cartprod @ sK2 @ sK4 ) )
& $false ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK3 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK3 ) ) ) ) ) )
@ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f1215,f592]) ).
thf(f592,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $false
= ( !! @ X0 @ X1 ) )
| ( $true
= ( X1 @ X2 ) ) ),
introduced(definition,[],[pi_proxy_axiom]) ).
thf(f3870,plain,
( spl6_87
| spl6_83
| ~ spl6_84 ),
inference(avatar_split_clause,[status(thm)],[f3865,f3781,f3759,f3867]) ).
thf(f3759,definition,
( spl6_83
<=> ( $true
= ( !! @ $o @ ( (=>) @ $true ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_83])],[avatar_definition]) ).
thf(f3781,definition,
( spl6_84
<=> ( $false
= ( sK0 @ $o @ ( (=>) @ $true ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_84])],[avatar_definition]) ).
thf(f3865,plain,
( ( $false
= ( $true
=> $false ) )
| spl6_83
| ~ spl6_84 ),
inference(subsumption_resolution,[status(thm)],[f3863,f3760]) ).
thf(f3760,plain,
( ( $true
!= ( !! @ $o @ ( (=>) @ $true ) ) )
| spl6_83 ),
inference(avatar_component_clause,[status(thm)],[f3759]) ).
thf(f3863,plain,
( ( $false
= ( $true
=> $false ) )
| ( $true
= ( !! @ $o @ ( (=>) @ $true ) ) )
| ~ spl6_84 ),
inference(superposition,[status(thm)],[f591,f3783]) ).
thf(f3783,plain,
( ( $false
= ( sK0 @ $o @ ( (=>) @ $true ) ) )
| ~ spl6_84 ),
inference(avatar_component_clause,[status(thm)],[f3781]) ).
thf(f591,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( X1 @ ( sK0 @ X0 @ X1 ) )
= $false )
| ( $true
= ( !! @ X0 @ X1 ) ) ),
introduced(definition,[],[pi_proxy_axiom]) ).
thf(f3841,plain,
( spl6_23
| ~ spl6_85 ),
inference(avatar_split_clause,[status(thm)],[f3837,f3799,f1625]) ).
thf(f1625,definition,
( spl6_23
<=> ! [X0: $o] : ( $true = X0 ) ),
introduced(definition,[new_symbols(naming,[spl6_23])],[avatar_definition]) ).
thf(f3799,definition,
( spl6_85
<=> ! [X0: $o] :
( $true
= ( $true
=> X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_85])],[avatar_definition]) ).
thf(f3837,plain,
( ! [X0: $o] : ( $true = X0 )
| ~ spl6_85 ),
inference(trivial_inequality_removal,[status(thm)],[f3836]) ).
thf(f3836,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true = $false ) )
| ~ spl6_85 ),
inference(duplicate_literal_removal,[status(thm)],[f3830]) ).
thf(f3830,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true = $false )
| ( $true = $false ) )
| ~ spl6_85 ),
inference(superposition,[status(thm)],[f3800,f597]) ).
thf(f597,plain,
! [X2: $o,X1: $o] :
( ( $false
= ( X1
=> X2 ) )
| ( $false = X1 )
| ( $true = X2 ) ),
introduced(definition,[],[implies_proxy_axiom]) ).
thf(f3800,plain,
( ! [X0: $o] :
( $true
= ( $true
=> X0 ) )
| ~ spl6_85 ),
inference(avatar_component_clause,[status(thm)],[f3799]) ).
thf(f3802,plain,
( spl6_85
| ~ spl6_83 ),
inference(avatar_split_clause,[status(thm)],[f3796,f3759,f3799]) ).
thf(f3796,plain,
( ! [X0: $o] :
( $true
= ( $true
=> X0 ) )
| ~ spl6_83 ),
inference(trivial_inequality_removal,[status(thm)],[f3794]) ).
thf(f3794,plain,
( ! [X0: $o] :
( ( $true
= ( $true
=> X0 ) )
| ( $true = $false ) )
| ~ spl6_83 ),
inference(superposition,[status(thm)],[f3761,f592]) ).
thf(f3761,plain,
( ( $true
= ( !! @ $o @ ( (=>) @ $true ) ) )
| ~ spl6_83 ),
inference(avatar_component_clause,[status(thm)],[f3759]) ).
thf(f3785,plain,
( spl6_84
| ~ spl6_82 ),
inference(avatar_split_clause,[status(thm)],[f3777,f3755,f3781]) ).
thf(f3755,definition,
( spl6_82
<=> ( $true
= ( ( sK0 @ $o @ ( (=>) @ $true ) )
=> $false ) ) ),
introduced(definition,[new_symbols(naming,[spl6_82])],[avatar_definition]) ).
thf(f3777,plain,
( ( $false
= ( sK0 @ $o @ ( (=>) @ $true ) ) )
| ~ spl6_82 ),
inference(trivial_inequality_removal,[status(thm)],[f3776]) ).
thf(f3776,plain,
( ( $false
= ( sK0 @ $o @ ( (=>) @ $true ) ) )
| ( $true = $false )
| ~ spl6_82 ),
inference(duplicate_literal_removal,[status(thm)],[f3775]) ).
thf(f3775,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ $o @ ( (=>) @ $true ) ) )
| ( $true = $false )
| ~ spl6_82 ),
inference(superposition,[status(thm)],[f597,f3757]) ).
thf(f3757,plain,
( ( $true
= ( ( sK0 @ $o @ ( (=>) @ $true ) )
=> $false ) )
| ~ spl6_82 ),
inference(avatar_component_clause,[status(thm)],[f3755]) ).
thf(f3763,plain,
( spl6_82
| spl6_83 ),
inference(avatar_split_clause,[status(thm)],[f3748,f3759,f3755]) ).
thf(f3748,plain,
( ( $true
= ( ( sK0 @ $o @ ( (=>) @ $true ) )
=> $false ) )
| ( $true
= ( !! @ $o @ ( (=>) @ $true ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3747]) ).
thf(f3747,plain,
( ( $true = $false )
| ( $true
= ( ( sK0 @ $o @ ( (=>) @ $true ) )
=> $false ) )
| ( $true
= ( !! @ $o @ ( (=>) @ $true ) ) ) ),
inference(superposition,[status(thm)],[f591,f3730]) ).
thf(f3730,plain,
! [X0: $o] :
( ( $true
= ( $true
=> X0 ) )
| ( $true
= ( X0
=> $false ) ) ),
inference(superposition,[status(thm)],[f1588,f3589]) ).
thf(f3589,plain,
! [X0: $i,X1: $o] :
( ( $false
= ( in @ X0 @ ( prop2set @ X1 ) ) )
| ( ( $true
=> X1 )
= $true ) ),
inference(fool_paramodulation,[status(thm)],[f3581]) ).
thf(f3581,plain,
! [X0: $i,X1: $o] :
( $true
= ( ( in @ X0 @ ( prop2set @ X1 ) )
=> X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f3580]) ).
thf(f3580,plain,
! [X0: $i,X1: $o] :
( $true
= ( ^ [Y0: $o] :
( ( in @ X0 @ ( prop2set @ Y0 ) )
=> Y0 )
@ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f3576]) ).
thf(f3576,plain,
! [X0: $i,X1: $o] :
( ( $true
= ( ^ [Y0: $o] :
( ( in @ X0 @ ( prop2set @ Y0 ) )
=> Y0 )
@ X1 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f1801,f592]) ).
thf(f1801,plain,
! [X0: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( in @ X0 @ ( prop2set @ Y0 ) )
=> Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1800]) ).
thf(f1800,plain,
! [X0: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ ( prop2set @ Y1 ) )
=> Y1 ) )
@ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1797]) ).
thf(f1797,plain,
! [X0: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ ( prop2set @ Y1 ) )
=> Y1 ) )
@ X0 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f592,f1126]) ).
thf(f1126,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ ( prop2set @ Y1 ) )
=> Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f925,f721]) ).
thf(f721,plain,
prop2setE = $true,
inference(cnf_transformation,[status(thm)],[f608]) ).
thf(f925,plain,
( prop2setE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ ( prop2set @ Y1 ) )
=> Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f530]) ).
thf(f530,plain,
( prop2setE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ ( prop2set @ Y1 ) )
=> Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f529]) ).
thf(f529,plain,
( prop2setE
= ( ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,axiom,
( prop2setE
= ( ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',prop2setE) ).
thf(f1588,plain,
! [X0: $o] :
( $true
= ( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1587]) ).
thf(f1587,plain,
! [X0: $o] :
( $true
= ( ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) )
@ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1584]) ).
thf(f1584,plain,
! [X0: $o] :
( ( $true
= ( ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) )
@ X0 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f592,f1069]) ).
thf(f1069,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f761,f610]) ).
thf(f610,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f540]) ).
thf(f540,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f539]) ).
thf(f539,plain,
! [X0: $o] :
( ( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) )
= prop2setI ),
inference(rectify,[status(thm)],[f59]) ).
thf(f59,axiom,
! [X0: $o] :
( ( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) )
= prop2setI ),
file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',prop2setI) ).
thf(f761,plain,
prop2setI = $true,
inference(cnf_transformation,[status(thm)],[f608]) ).
thf(f1668,plain,
( spl6_19
| ~ spl6_23 ),
inference(avatar_split_clause,[status(thm)],[f1662,f1625,f1500]) ).
thf(f1500,definition,
( spl6_19
<=> ! [X0: $o] : ( $false = X0 ) ),
introduced(definition,[new_symbols(naming,[spl6_19])],[avatar_definition]) ).
thf(f1662,plain,
( ! [X0: $o] : ( $false = X0 )
| ~ spl6_23 ),
inference(trivial_inequality_removal,[status(thm)],[f1643]) ).
thf(f1643,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 ) )
| ~ spl6_23 ),
inference(superposition,[status(thm)],[f590,f1626]) ).
thf(f1626,plain,
( ! [X0: $o] : ( $true = X0 )
| ~ spl6_23 ),
inference(avatar_component_clause,[status(thm)],[f1625]) ).
thf(f590,plain,
! [X1: $o] :
( ( $false = ( ~ X1 ) )
| ( $false = X1 ) ),
introduced(definition,[],[logical_not_proxy_axiom]) ).
thf(f1654,plain,
( spl6_4
| ~ spl6_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f1653]) ).
thf(f1653,plain,
( $false
| spl6_4
| ~ spl6_23 ),
inference(trivial_inequality_removal,[status(thm)],[f1649]) ).
thf(f1649,plain,
( ( $true != $true )
| spl6_4
| ~ spl6_23 ),
inference(superposition,[status(thm)],[f1362,f1626]) ).
thf(f1362,plain,
( ( ( !! @ $o @ (~) )
!= $true )
| spl6_4 ),
inference(avatar_component_clause,[status(thm)],[f1361]) ).
thf(f1361,definition,
( spl6_4
<=> ( ( !! @ $o @ (~) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition]) ).
thf(f1536,plain,
( spl6_18
| ~ spl6_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f1535]) ).
thf(f1535,plain,
( $false
| spl6_18
| ~ spl6_19 ),
inference(subsumption_resolution,[status(thm)],[f1480,f1501]) ).
thf(f1501,plain,
( ! [X0: $o] : ( $false = X0 )
| ~ spl6_19 ),
inference(avatar_component_clause,[status(thm)],[f1500]) ).
thf(f1480,plain,
( ( ( !! @ $o @ (~) )
!= $false )
| spl6_18 ),
inference(avatar_component_clause,[status(thm)],[f1479]) ).
thf(f1479,definition,
( spl6_18
<=> ( ( !! @ $o @ (~) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl6_18])],[avatar_definition]) ).
thf(f1531,plain,
( ~ spl6_4
| ~ spl6_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f1530]) ).
thf(f1530,plain,
( $false
| ~ spl6_4
| ~ spl6_18 ),
inference(trivial_inequality_removal,[status(thm)],[f1529]) ).
thf(f1529,plain,
( ( $true = $false )
| ~ spl6_4
| ~ spl6_18 ),
inference(forward_demodulation,[status(thm)],[f1363,f1481]) ).
thf(f1481,plain,
( ( ( !! @ $o @ (~) )
= $false )
| ~ spl6_18 ),
inference(avatar_component_clause,[status(thm)],[f1479]) ).
thf(f1363,plain,
( ( ( !! @ $o @ (~) )
= $true )
| ~ spl6_4 ),
inference(avatar_component_clause,[status(thm)],[f1361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU672^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n022.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:30:36 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU672^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Functions
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : (! A:i.! B:i.! f:i.func A B f -> (! x:i.in x A -> singleton
% 0.16/0.39 % (dsetconstr B (^ y:i.in (kpair x y) f))))
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC174g [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.46 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 419 ( 195 unt; 223 typ; 195 def)
% 0.16/0.39 % Number of atoms : 1031 ( 288 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 192 ( 5 avg)
% 0.16/0.39 % Number of connectives : 1854 ( 47 ~; 7 |; 36 &;1297 @)
% 0.16/0.39 % ( 14 <=>; 453 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 202 ( 2 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 111 ( 111 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 226 ( 223 usr; 192 con; 0-3 aty)
% 0.16/0.39 % Number of variables : 602 ( 65 ^; 501 !; 36 ?; 602 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=223
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu_type,type,
% 0.16/0.39 exu: ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu,definition,
% 0.16/0.39 ( exu
% 0.16/0.39 = ( ^ [Xphi: $i > $o] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx_type,type,
% 0.16/0.39 setextAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx,definition,
% 0.16/0.39 ( setextAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xx @ B ) )
% 0.16/0.39 => ( A = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset_type,type,
% 0.16/0.39 emptyset: $i ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx_type,type,
% 0.16/0.39 emptysetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx,definition,
% 0.16/0.39 ( emptysetAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin_type,type,
% 0.16/0.39 setadjoin: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx_type,type,
% 0.16/0.39 setadjoinAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx,definition,
% 0.16/0.39 ( setadjoinAx
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 <=> ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset_type,type,
% 0.16/0.39 powerset: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx_type,type,
% 0.16/0.39 powersetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx,definition,
% 0.16/0.39 ( powersetAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 <=> ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion_type,type,
% 0.16/0.39 setunion: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx_type,type,
% 0.16/0.39 setunionAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx,definition,
% 0.16/0.39 ( setunionAx
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 <=> ? [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega_type,type,
% 0.16/0.39 omega: $i ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax_type,type,
% 0.16/0.39 omega0Ax: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax,definition,
% 0.16/0.39 ( omega0Ax
% 0.16/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx_type,type,
% 0.16/0.39 omegaSAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx,definition,
% 0.16/0.39 ( omegaSAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx_type,type,
% 0.16/0.39 omegaIndAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx,definition,
% 0.16/0.39 ( omegaIndAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( ( in @ emptyset @ A )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ omega )
% 0.16/0.39 & ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(replAx_type,type,
% 0.16/0.39 replAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(replAx,definition,
% 0.16/0.39 ( replAx
% 0.16/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 <=> ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx_type,type,
% 0.16/0.39 foundationAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx,definition,
% 0.16/0.39 ( foundationAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ( ( in @ B @ A )
% 0.16/0.39 & ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx_type,type,
% 0.16/0.39 wellorderingAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx,definition,
% 0.16/0.39 ( wellorderingAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ? [B: $i] :
% 0.16/0.39 ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) ) )
% 0.16/0.39 & ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ A )
% 0.16/0.39 & ( in @ Xy @ A ) )
% 0.16/0.39 => ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ( ( in @ Xx @ C )
% 0.16/0.39 <=> ( in @ Xy @ C ) ) )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 & ! [C: $i,D: $i] :
% 0.16/0.39 ( ( ( in @ C @ B )
% 0.16/0.39 & ( in @ D @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ D ) )
% 0.16/0.39 | ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ D )
% 0.16/0.39 => ( in @ Xx @ C ) ) ) )
% 0.16/0.39 & ! [C: $i] :
% 0.16/0.39 ( ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.39 => ? [D: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ D @ B )
% 0.16/0.39 & ( in @ Xx @ C )
% 0.16/0.39 & ~ ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ D )
% 0.16/0.39 & ( in @ Xy @ C ) )
% 0.16/0.39 & ! [E: $i] :
% 0.16/0.39 ( ( in @ E @ B )
% 0.16/0.39 => ( ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ E )
% 0.16/0.39 => ( in @ Xy @ D ) )
% 0.16/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr_type,type,
% 0.16/0.39 descr: ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(descrp_type,type,
% 0.16/0.39 descrp: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descrp,definition,
% 0.16/0.39 ( descrp
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( Xphi
% 0.16/0.39 @ ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr_type,type,
% 0.16/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI_type,type,
% 0.16/0.39 dsetconstrI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI,definition,
% 0.16/0.39 ( dsetconstrI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL_type,type,
% 0.16/0.39 dsetconstrEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL,definition,
% 0.16/0.39 ( dsetconstrEL
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER_type,type,
% 0.16/0.39 dsetconstrER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER,definition,
% 0.16/0.39 ( dsetconstrER
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1_type,type,
% 0.16/0.39 exuE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1,definition,
% 0.16/0.39 ( exuE1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set_type,type,
% 0.16/0.39 prop2set: $o > $i ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE_type,type,
% 0.16/0.39 prop2setE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE,definition,
% 0.16/0.39 ( prop2setE
% 0.16/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE_type,type,
% 0.16/0.39 emptysetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE,definition,
% 0.16/0.39 ( emptysetE
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse_type,type,
% 0.16/0.39 emptysetimpfalse: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse,definition,
% 0.16/0.39 ( emptysetimpfalse
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => $false ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset_type,type,
% 0.16/0.39 notinemptyset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset,definition,
% 0.16/0.39 ( notinemptyset
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e_type,type,
% 0.16/0.39 exuE3e: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e,definition,
% 0.16/0.39 ( exuE3e
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setext_type,type,
% 0.16/0.39 setext: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setext,definition,
% 0.16/0.39 ( setext
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( A = B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI_type,type,
% 0.16/0.39 emptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI,definition,
% 0.16/0.39 ( emptyI
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty_type,type,
% 0.16/0.39 noeltsimpempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty,definition,
% 0.16/0.39 ( noeltsimpempty
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta_type,type,
% 0.16/0.39 setbeta: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta,definition,
% 0.16/0.39 ( setbeta
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty_type,type,
% 0.16/0.39 nonempty: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty,definition,
% 0.16/0.39 ( nonempty
% 0.16/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1_type,type,
% 0.16/0.39 nonemptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1,definition,
% 0.16/0.39 ( nonemptyE1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI_type,type,
% 0.16/0.39 nonemptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI,definition,
% 0.16/0.39 ( nonemptyI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( nonempty
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1_type,type,
% 0.16/0.39 nonemptyI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1,definition,
% 0.16/0.39 ( nonemptyI1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ( nonempty @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL_type,type,
% 0.16/0.39 setadjoinIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL,definition,
% 0.16/0.39 ( setadjoinIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty_type,type,
% 0.16/0.39 emptyinunitempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty,definition,
% 0.16/0.39 ( emptyinunitempty
% 0.16/0.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR_type,type,
% 0.16/0.39 setadjoinIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR,definition,
% 0.16/0.39 ( setadjoinIR
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE_type,type,
% 0.16/0.39 setadjoinE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE,definition,
% 0.16/0.39 ( setadjoinE
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ( ( Xy = Xx )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => ( ( ( in @ Xy @ A )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr_type,type,
% 0.16/0.39 setadjoinOr: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr,definition,
% 0.16/0.39 ( setadjoinOr
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq_type,type,
% 0.16/0.39 setoftrueEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq,definition,
% 0.16/0.39 ( setoftrueEq
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : $true )
% 0.16/0.39 = A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI_type,type,
% 0.16/0.39 powersetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI,definition,
% 0.16/0.39 ( powersetI
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset_type,type,
% 0.16/0.39 emptyinPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset,definition,
% 0.16/0.39 ( emptyinPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset_type,type,
% 0.16/0.39 emptyInPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset,definition,
% 0.16/0.39 ( emptyInPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE_type,type,
% 0.16/0.39 powersetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE,definition,
% 0.16/0.39 ( powersetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI_type,type,
% 0.16/0.39 setunionI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI,definition,
% 0.16/0.39 ( setunionI
% 0.16/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE_type,type,
% 0.16/0.39 setunionE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE,definition,
% 0.16/0.39 ( setunionE
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ! [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU_type,type,
% 0.16/0.39 subPowSU: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU,definition,
% 0.16/0.39 ( subPowSU
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2_type,type,
% 0.16/0.39 exuE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2,definition,
% 0.16/0.39 ( exuE2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness_type,type,
% 0.16/0.39 nonemptyImpWitness: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness,definition,
% 0.16/0.39 ( nonemptyImpWitness
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & $true ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit_type,type,
% 0.16/0.39 uniqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit,definition,
% 0.16/0.39 ( uniqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton_type,type,
% 0.16/0.39 notinsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton,definition,
% 0.16/0.39 ( notinsingleton
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx != Xy )
% 0.16/0.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit_type,type,
% 0.16/0.39 eqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit,definition,
% 0.16/0.39 ( eqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch_type,type,
% 0.16/0.39 singletonsswitch: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch,definition,
% 0.16/0.39 ( singletonsswitch
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE_type,type,
% 0.16/0.39 upairsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE,definition,
% 0.16/0.39 ( upairsetE
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.39 => ( ( Xz = Xx )
% 0.16/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL_type,type,
% 0.16/0.39 upairsetIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL,definition,
% 0.16/0.39 ( upairsetIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR_type,type,
% 0.16/0.39 upairsetIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR,definition,
% 0.16/0.39 ( upairsetIR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1_type,type,
% 0.16/0.39 emptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1,definition,
% 0.16/0.39 ( emptyE1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = emptyset )
% 0.16/0.39 => $false ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall_type,type,
% 0.16/0.39 vacuousDall: $o ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall,definition,
% 0.16/0.39 ( vacuousDall
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1_type,type,
% 0.16/0.39 quantDeMorgan1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1,definition,
% 0.16/0.39 ( quantDeMorgan1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2_type,type,
% 0.16/0.39 quantDeMorgan2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2,definition,
% 0.16/0.39 ( quantDeMorgan2
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3_type,type,
% 0.16/0.39 quantDeMorgan3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3,definition,
% 0.16/0.39 ( quantDeMorgan3
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4_type,type,
% 0.16/0.39 quantDeMorgan4: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4,definition,
% 0.16/0.39 ( quantDeMorgan4
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI_type,type,
% 0.16/0.39 prop2setI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI,definition,
% 0.16/0.39 ( prop2setI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(set2prop_type,type,
% 0.16/0.39 set2prop: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI_type,type,
% 0.16/0.39 prop2set2propI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI,definition,
% 0.16/0.39 ( prop2set2propI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE_type,type,
% 0.16/0.39 notdexE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE,definition,
% 0.16/0.39 ( notdexE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE_type,type,
% 0.16/0.39 notdallE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE,definition,
% 0.16/0.39 ( notdallE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1_type,type,
% 0.16/0.39 exuI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1,definition,
% 0.16/0.39 ( exuI1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3_type,type,
% 0.16/0.39 exuI3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3,definition,
% 0.16/0.39 ( exuI3
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.16/0.39 => ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2_type,type,
% 0.16/0.39 exuI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2,definition,
% 0.16/0.39 ( exuI2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP_type,type,
% 0.16/0.39 inCongP: $o ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP,definition,
% 0.16/0.39 ( inCongP
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong_type,type,
% 0.16/0.39 in__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong,definition,
% 0.16/0.39 ( in__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u_type,type,
% 0.16/0.39 exuE3u: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u,definition,
% 0.16/0.39 ( exuE3u
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong_type,type,
% 0.16/0.39 exu__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong,definition,
% 0.16/0.39 ( exu__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 <=> ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong_type,type,
% 0.16/0.39 emptyset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong,definition,
% 0.16/0.39 ( emptyset__Cong
% 0.16/0.39 = ( emptyset = emptyset ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong_type,type,
% 0.16/0.39 setadjoin__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong,definition,
% 0.16/0.39 ( setadjoin__Cong
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ! [Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( Xz = Xu )
% 0.16/0.39 => ( ( setadjoin @ Xx @ Xz )
% 0.16/0.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong_type,type,
% 0.16/0.39 powerset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong,definition,
% 0.16/0.39 ( powerset__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( powerset @ A )
% 0.16/0.39 = ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong_type,type,
% 0.16/0.39 setunion__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong,definition,
% 0.16/0.39 ( setunion__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( setunion @ A )
% 0.16/0.39 = ( setunion @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong_type,type,
% 0.16/0.39 omega__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong,definition,
% 0.16/0.39 ( omega__Cong
% 0.16/0.39 = ( omega = omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu_type,type,
% 0.16/0.39 exuEu: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu,definition,
% 0.16/0.39 ( exuEu
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong_type,type,
% 0.16/0.39 descr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong,definition,
% 0.16/0.39 ( descr__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.16/0.39 => ( ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong_type,type,
% 0.16/0.39 dsetconstr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong,definition,
% 0.16/0.39 ( dsetconstr__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.16/0.39 => ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( dsetconstr @ B
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subset_type,type,
% 0.16/0.39 subset: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(disjoint_type,type,
% 0.16/0.39 disjoint: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(setsmeet_type,type,
% 0.16/0.39 setsmeet: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1_type,type,
% 0.16/0.39 subsetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1,definition,
% 0.16/0.39 ( subsetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2_type,type,
% 0.16/0.39 eqimpsubset2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2,definition,
% 0.16/0.39 ( eqimpsubset2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1_type,type,
% 0.16/0.39 eqimpsubset1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1,definition,
% 0.16/0.39 ( eqimpsubset1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2_type,type,
% 0.16/0.39 subsetI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2,definition,
% 0.16/0.39 ( subsetI2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset_type,type,
% 0.16/0.39 emptysetsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset,definition,
% 0.16/0.39 ( emptysetsubset
% 0.16/0.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE_type,type,
% 0.16/0.39 subsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE,definition,
% 0.16/0.39 ( subsetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2_type,type,
% 0.16/0.39 subsetE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2,definition,
% 0.16/0.39 ( subsetE2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI_type,type,
% 0.16/0.39 notsubsetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI,definition,
% 0.16/0.39 ( notsubsetI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1_type,type,
% 0.16/0.39 notequalI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1,definition,
% 0.16/0.39 ( notequalI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ~ ( subset @ A @ B )
% 0.16/0.39 => ( A != B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI2_type,type,
% 0.16/0.39 notequalI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI2,definition,
% 0.16/0.39 ( notequalI2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ( A != B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetRefl_type,type,
% 0.16/0.39 subsetRefl: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetRefl,definition,
% 0.16/0.39 ( subsetRefl
% 0.16/0.39 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetTrans_type,type,
% 0.16/0.39 subsetTrans: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetTrans,definition,
% 0.16/0.39 ( subsetTrans
% 0.16/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( subset @ B @ C )
% 0.16/0.39 => ( subset @ A @ C ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub_type,type,
% 0.16/0.39 setadjoinSub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub,definition,
% 0.16/0.39 ( setadjoinSub
% 0.16/0.39 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub2_type,type,
% 0.16/0.39 setadjoinSub2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub2,definition,
% 0.16/0.39 ( setadjoinSub2
% 0.16/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subset2powerset_type,type,
% 0.16/0.39 subset2powerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subset2powerset,definition,
% 0.16/0.39 ( subset2powerset
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextsub_type,type,
% 0.16/0.39 setextsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setextsub,definition,
% 0.16/0.39 ( setextsub
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( subset @ B @ A )
% 0.16/0.39 => ( A = B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetemptysetimpeq_type,type,
% 0.16/0.39 subsetemptysetimpeq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetemptysetimpeq,definition,
% 0.16/0.39 ( subsetemptysetimpeq
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( subset @ A @ emptyset )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI1_type,type,
% 0.16/0.39 powersetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI1,definition,
% 0.16/0.39 ( powersetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ B @ A )
% 0.16/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE1_type,type,
% 0.16/0.39 powersetE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE1,definition,
% 0.16/0.39 ( powersetE1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(inPowerset_type,type,
% 0.16/0.39 inPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(inPowerset,definition,
% 0.16/0.39 ( inPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetsubset_type,type,
% 0.16/0.39 powersetsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetsubset,definition,
% 0.16/0.39 ( powersetsubset
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sepInPowerset_type,type,
% 0.16/0.39 sepInPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(sepInPowerset,definition,
% 0.16/0.39 ( sepInPowerset
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( in
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sepSubset_type,type,
% 0.16/0.39 sepSubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(sepSubset,definition,
% 0.16/0.39 ( sepSubset
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( subset
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunion_type,type,
% 0.16/0.39 binunion: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIL_type,type,
% 0.16/0.39 binunionIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIL,definition,
% 0.16/0.39 ( binunionIL
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2IR_type,type,
% 0.16/0.39 upairset2IR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2IR,definition,
% 0.16/0.39 ( upairset2IR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIR_type,type,
% 0.16/0.39 binunionIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIR,definition,
% 0.16/0.39 ( binunionIR
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionEcases_type,type,
% 0.16/0.39 binunionEcases: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionEcases,definition,
% 0.16/0.39 ( binunionEcases
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.16/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.39 => ( ( ( in @ Xx @ A )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => ( ( ( in @ Xx @ B )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionE_type,type,
% 0.16/0.39 binunionE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionE,definition,
% 0.16/0.39 ( binunionE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionLsub_type,type,
% 0.16/0.39 binunionLsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionLsub,definition,
% 0.16/0.39 ( binunionLsub
% 0.16/0.39 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionRsub_type,type,
% 0.16/0.39 binunionRsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionRsub,definition,
% 0.16/0.39 ( binunionRsub
% 0.16/0.39 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersect_type,type,
% 0.16/0.39 binintersect: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectI_type,type,
% 0.16/0.39 binintersectI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectI,definition,
% 0.16/0.39 ( binintersectI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset5_type,type,
% 0.16/0.39 binintersectSubset5: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset5,definition,
% 0.16/0.39 ( binintersectSubset5
% 0.16/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.39 ( ( subset @ C @ A )
% 0.16/0.39 => ( ( subset @ C @ B )
% 0.16/0.39 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectEL_type,type,
% 0.16/0.39 binintersectEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectEL,definition,
% 0.16/0.39 ( binintersectEL
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectLsub_type,type,
% 0.16/0.39 binintersectLsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectLsub,definition,
% 0.16/0.39 ( binintersectLsub
% 0.16/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset2_type,type,
% 0.16/0.39 binintersectSubset2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset2,definition,
% 0.16/0.39 ( binintersectSubset2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( binintersect @ A @ B )
% 0.16/0.39 = A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset3_type,type,
% 0.16/0.39 binintersectSubset3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset3,definition,
% 0.16/0.39 ( binintersectSubset3
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( ( binintersect @ A @ B )
% 0.16/0.39 = B )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectER_type,type,
% 0.16/0.39 binintersectER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectER,definition,
% 0.16/0.39 ( binintersectER
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.16/0.39 => ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(disjointsetsI1_type,type,
% 0.16/0.39 disjointsetsI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(disjointsetsI1,definition,
% 0.16/0.39 ( disjointsetsI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( in @ Xx @ B ) )
% 0.16/0.39 => ( ( binintersect @ A @ B )
% 0.16/0.39 = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectRsub_type,type,
% 0.16/0.39 binintersectRsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectRsub,definition,
% 0.16/0.39 ( binintersectRsub
% 0.16/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset4_type,type,
% 0.16/0.39 binintersectSubset4: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset4,definition,
% 0.16/0.39 ( binintersectSubset4
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ B @ A )
% 0.16/0.39 => ( ( binintersect @ A @ B )
% 0.16/0.39 = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset1_type,type,
% 0.16/0.39 binintersectSubset1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset1,definition,
% 0.16/0.39 ( binintersectSubset1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( ( binintersect @ A @ B )
% 0.16/0.39 = A )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(bs114d_type,type,
% 0.16/0.39 bs114d: $o ).
% 0.16/0.39
% 0.16/0.39 thf(bs114d,definition,
% 0.16/0.39 ( bs114d
% 0.16/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.39 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.16/0.39 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(regular_type,type,
% 0.16/0.39 regular: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminus_type,type,
% 0.16/0.39 setminus: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setminusI_type,type,
% 0.16/0.39 setminusI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusI,definition,
% 0.16/0.39 ( setminusI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusEL_type,type,
% 0.16/0.39 setminusEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusEL,definition,
% 0.16/0.39 ( setminusEL
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusER_type,type,
% 0.16/0.39 setminusER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusER,definition,
% 0.16/0.39 ( setminusER
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.39 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusSubset2_type,type,
% 0.16/0.39 setminusSubset2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusSubset2,definition,
% 0.16/0.39 ( setminusSubset2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( setminus @ A @ B )
% 0.16/0.39 = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusERneg_type,type,
% 0.16/0.39 setminusERneg: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusERneg,definition,
% 0.16/0.39 ( setminusERneg
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusELneg_type,type,
% 0.16/0.39 setminusELneg: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusELneg,definition,
% 0.16/0.39 ( setminusELneg
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusILneg_type,type,
% 0.16/0.39 setminusILneg: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusILneg,definition,
% 0.16/0.39 ( setminusILneg
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ A )
% 0.16/0.39 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusIRneg_type,type,
% 0.16/0.39 setminusIRneg: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusIRneg,definition,
% 0.16/0.39 ( setminusIRneg
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusLsub_type,type,
% 0.16/0.39 setminusLsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusLsub,definition,
% 0.16/0.39 ( setminusLsub
% 0.16/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusSubset1_type,type,
% 0.16/0.39 setminusSubset1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusSubset1,definition,
% 0.16/0.39 ( setminusSubset1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( ( setminus @ A @ B )
% 0.16/0.39 = emptyset )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiff_type,type,
% 0.16/0.39 symdiff: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffE_type,type,
% 0.16/0.39 symdiffE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffE,definition,
% 0.16/0.39 ( symdiffE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => Xphi ) )
% 0.16/0.39 => ( ( ~ ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffI1_type,type,
% 0.16/0.39 symdiffI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffI1,definition,
% 0.16/0.39 ( symdiffI1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffI2_type,type,
% 0.16/0.39 symdiffI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffI2,definition,
% 0.16/0.39 ( symdiffI2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffIneg1_type,type,
% 0.16/0.39 symdiffIneg1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffIneg1,definition,
% 0.16/0.39 ( symdiffIneg1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffIneg2_type,type,
% 0.16/0.39 symdiffIneg2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffIneg2,definition,
% 0.16/0.39 ( symdiffIneg2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(iskpair_type,type,
% 0.16/0.39 iskpair: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(secondinupair_type,type,
% 0.16/0.39 secondinupair: $o ).
% 0.16/0.39
% 0.16/0.39 thf(secondinupair,definition,
% 0.16/0.39 ( secondinupair
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairIL_type,type,
% 0.16/0.39 setukpairIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairIL,definition,
% 0.16/0.39 ( setukpairIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairIR_type,type,
% 0.16/0.39 setukpairIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairIR,definition,
% 0.16/0.39 ( setukpairIR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kpairiskpair_type,type,
% 0.16/0.39 kpairiskpair: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kpairiskpair,definition,
% 0.16/0.39 ( kpairiskpair
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kpair_type,type,
% 0.16/0.39 kpair: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(kpairp_type,type,
% 0.16/0.39 kpairp: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kpairp,definition,
% 0.16/0.39 ( kpairp
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprod_type,type,
% 0.16/0.39 cartprod: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsubset_type,type,
% 0.16/0.39 singletonsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsubset,definition,
% 0.16/0.39 ( singletonsubset
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletoninpowerset_type,type,
% 0.16/0.39 singletoninpowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletoninpowerset,definition,
% 0.16/0.39 ( singletoninpowerset
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletoninpowunion_type,type,
% 0.16/0.39 singletoninpowunion: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletoninpowunion,definition,
% 0.16/0.39 ( singletoninpowunion
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2E_type,type,
% 0.16/0.39 upairset2E: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2E,definition,
% 0.16/0.39 ( upairset2E
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.39 => ( ( Xz = Xx )
% 0.16/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsubunion_type,type,
% 0.16/0.39 upairsubunion: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsubunion,definition,
% 0.16/0.39 ( upairsubunion
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairinpowunion_type,type,
% 0.16/0.39 upairinpowunion: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairinpowunion,definition,
% 0.16/0.39 ( upairinpowunion
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem1_type,type,
% 0.16/0.39 ubforcartprodlem1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem1,definition,
% 0.16/0.39 ( ubforcartprodlem1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem2_type,type,
% 0.16/0.39 ubforcartprodlem2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem2,definition,
% 0.16/0.39 ( ubforcartprodlem2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem3_type,type,
% 0.16/0.39 ubforcartprodlem3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem3,definition,
% 0.16/0.39 ( ubforcartprodlem3
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairin_type,type,
% 0.16/0.39 cartprodpairin: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairin,definition,
% 0.16/0.39 ( cartprodpairin
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempair1_type,type,
% 0.16/0.39 cartprodmempair1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempair1,definition,
% 0.16/0.39 ( cartprodmempair1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 & ( Xu
% 0.16/0.39 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempair_type,type,
% 0.16/0.39 cartprodmempair: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempair,definition,
% 0.16/0.39 ( cartprodmempair
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( iskpair @ Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE2_type,type,
% 0.16/0.39 setunionE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE2,definition,
% 0.16/0.39 ( setunionE2
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 => ? [X: $i] :
% 0.16/0.39 ( ( in @ X @ A )
% 0.16/0.39 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton1_type,type,
% 0.16/0.39 setunionsingleton1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton1,definition,
% 0.16/0.39 ( setunionsingleton1
% 0.16/0.39 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton2_type,type,
% 0.16/0.39 setunionsingleton2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton2,definition,
% 0.16/0.39 ( setunionsingleton2
% 0.16/0.39 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton_type,type,
% 0.16/0.39 setunionsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton,definition,
% 0.16/0.39 ( setunionsingleton
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.16/0.39 = Xx ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singleton_type,type,
% 0.16/0.39 singleton: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(singleton,definition,
% 0.16/0.39 ( singleton
% 0.16/0.39 = ( ^ [A: $i] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( A
% 0.16/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletonprop_type,type,
% 0.16/0.39 singletonprop: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonprop,definition,
% 0.16/0.39 ( singletonprop
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) )
% 0.16/0.39 => ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ( singleton
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1_type,type,
% 0.16/0.39 ex1: $i > ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1,definition,
% 0.16/0.39 ( ex1
% 0.16/0.39 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( singleton
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1E1_type,type,
% 0.16/0.39 ex1E1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1E1,definition,
% 0.16/0.39 ( ex1E1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ( ex1 @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1I_type,type,
% 0.16/0.39 ex1I: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1I,definition,
% 0.16/0.39 ( ex1I
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xy = Xx ) ) )
% 0.16/0.39 => ( ex1 @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1I2_type,type,
% 0.16/0.39 ex1I2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1I2,definition,
% 0.16/0.39 ( ex1I2
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) )
% 0.16/0.39 => ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ( ex1 @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsuniq_type,type,
% 0.16/0.39 singletonsuniq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsuniq,definition,
% 0.16/0.39 ( singletonsuniq
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ( setadjoin @ Xx @ emptyset )
% 0.16/0.39 = ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(atmost1p_type,type,
% 0.16/0.39 atmost1p: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(atleast2p_type,type,
% 0.16/0.39 atleast2p: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(atmost2p_type,type,
% 0.16/0.39 atmost2p: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetp_type,type,
% 0.16/0.39 upairsetp: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL1_type,type,
% 0.16/0.39 setukpairinjL1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL1,definition,
% 0.16/0.39 ( setukpairinjL1
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.16/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kfstsingleton_type,type,
% 0.16/0.39 kfstsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kfstsingleton,definition,
% 0.16/0.39 ( kfstsingleton
% 0.16/0.39 = ( ! [Xu: $i] :
% 0.16/0.39 ( ( iskpair @ Xu )
% 0.16/0.39 => ( singleton
% 0.16/0.39 @ ( dsetconstr @ ( setunion @ Xu )
% 0.16/0.39 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(theprop_type,type,
% 0.16/0.39 theprop: $o ).
% 0.16/0.39
% 0.16/0.39 thf(theprop,definition,
% 0.16/0.39 ( theprop
% 0.16/0.39 = ( ! [X: $i] :
% 0.16/0.39 ( ( singleton @ X )
% 0.16/0.39 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kfst_type,type,
% 0.16/0.39 kfst: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(kfstpairEq_type,type,
% 0.16/0.39 kfstpairEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kfstpairEq,definition,
% 0.16/0.39 ( kfstpairEq
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.16/0.39 = Xx ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodfstin_type,type,
% 0.16/0.39 cartprodfstin: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodfstin,definition,
% 0.16/0.39 ( cartprodfstin
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL2_type,type,
% 0.16/0.39 setukpairinjL2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL2,definition,
% 0.16/0.39 ( setukpairinjL2
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.16/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL_type,type,
% 0.16/0.39 setukpairinjL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL,definition,
% 0.16/0.39 ( setukpairinjL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( kpair @ Xx @ Xy )
% 0.16/0.39 = ( kpair @ Xz @ Xu ) )
% 0.16/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR11_type,type,
% 0.16/0.39 setukpairinjR11: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR11,definition,
% 0.16/0.39 ( setukpairinjR11
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR12_type,type,
% 0.16/0.39 setukpairinjR12: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR12,definition,
% 0.16/0.39 ( setukpairinjR12
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR1_type,type,
% 0.16/0.39 setukpairinjR1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR1,definition,
% 0.16/0.39 ( setukpairinjR1
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.16/0.39 => ( ( Xz = Xu )
% 0.16/0.39 => ( Xy = Xu ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairequniteq_type,type,
% 0.16/0.39 upairequniteq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairequniteq,definition,
% 0.16/0.39 ( upairequniteq
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ Xz @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR2_type,type,
% 0.16/0.39 setukpairinjR2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR2,definition,
% 0.16/0.39 ( setukpairinjR2
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.16/0.39 => ( Xy = Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR_type,type,
% 0.16/0.39 setukpairinjR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR,definition,
% 0.16/0.39 ( setukpairinjR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( kpair @ Xx @ Xy )
% 0.16/0.39 = ( kpair @ Xz @ Xu ) )
% 0.16/0.39 => ( Xy = Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ksndsingleton_type,type,
% 0.16/0.39 ksndsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ksndsingleton,definition,
% 0.16/0.39 ( ksndsingleton
% 0.16/0.39 = ( ! [Xu: $i] :
% 0.16/0.39 ( ( iskpair @ Xu )
% 0.16/0.39 => ( singleton
% 0.16/0.39 @ ( dsetconstr @ ( setunion @ Xu )
% 0.16/0.39 @ ^ [Xx: $i] :
% 0.16/0.39 ( Xu
% 0.16/0.39 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ksnd_type,type,
% 0.16/0.39 ksnd: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(ksndpairEq_type,type,
% 0.16/0.39 ksndpairEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ksndpairEq,definition,
% 0.16/0.39 ( ksndpairEq
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.16/0.39 = Xy ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kpairsurjEq_type,type,
% 0.16/0.39 kpairsurjEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kpairsurjEq,definition,
% 0.16/0.39 ( kpairsurjEq
% 0.16/0.39 = ( ! [Xu: $i] :
% 0.16/0.39 ( ( iskpair @ Xu )
% 0.16/0.39 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.16/0.39 = Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodsndin_type,type,
% 0.16/0.39 cartprodsndin: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodsndin,definition,
% 0.16/0.39 ( cartprodsndin
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairmemEL_type,type,
% 0.16/0.39 cartprodpairmemEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairmemEL,definition,
% 0.16/0.39 ( cartprodpairmemEL
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairmemER_type,type,
% 0.16/0.39 cartprodpairmemER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairmemER,definition,
% 0.16/0.39 ( cartprodpairmemER
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( in @ Xy @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempaircEq_type,type,
% 0.16/0.39 cartprodmempaircEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempaircEq,definition,
% 0.16/0.39 ( cartprodmempaircEq
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( kpair @ Xx @ Xy )
% 0.16/0.39 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodfstpairEq_type,type,
% 0.16/0.39 cartprodfstpairEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodfstpairEq,definition,
% 0.16/0.39 ( cartprodfstpairEq
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.16/0.39 = Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodsndpairEq_type,type,
% 0.16/0.39 cartprodsndpairEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodsndpairEq,definition,
% 0.16/0.39 ( cartprodsndpairEq
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.16/0.39 = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairsurjEq_type,type,
% 0.16/0.39 cartprodpairsurjEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairsurjEq,definition,
% 0.16/0.39 ( cartprodpairsurjEq
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.16/0.39 = Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(breln_type,type,
% 0.16/0.39 breln: $i > $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(breln,definition,
% 0.16/0.39 ( breln
% 0.16/0.39 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstr_type,type,
% 0.16/0.39 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrI_type,type,
% 0.16/0.39 dpsetconstrI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrI,definition,
% 0.16/0.39 ( dpsetconstrI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( Xphi @ Xx @ Xy )
% 0.16/0.39 => ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrSub_type,type,
% 0.16/0.39 dpsetconstrSub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrSub,definition,
% 0.16/0.39 ( dpsetconstrSub
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.16/0.39 ( subset
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.16/0.39 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setOfPairsIsBReln_type,type,
% 0.16/0.39 setOfPairsIsBReln: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setOfPairsIsBReln,definition,
% 0.16/0.39 ( setOfPairsIsBReln
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.16/0.39 ( breln @ A @ B
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrERa_type,type,
% 0.16/0.39 dpsetconstrERa: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrERa,definition,
% 0.16/0.39 ( dpsetconstrERa
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.16/0.39 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrEL1_type,type,
% 0.16/0.39 dpsetconstrEL1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrEL1,definition,
% 0.16/0.39 ( dpsetconstrEL1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrEL2_type,type,
% 0.16/0.39 dpsetconstrEL2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrEL2,definition,
% 0.16/0.39 ( dpsetconstrEL2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.16/0.39 => ( in @ Xy @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrER_type,type,
% 0.16/0.39 dpsetconstrER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrER,definition,
% 0.16/0.39 ( dpsetconstrER
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.16/0.39 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(func_type,type,
% 0.16/0.39 func: $i > $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(func,definition,
% 0.16/0.39 ( func
% 0.16/0.39 = ( ^ [A: $i,B: $i,R: $i] :
% 0.16/0.39 ( ( breln @ A @ B @ R )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ex1 @ B
% 0.16/0.39 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(funcSet_type,type,
% 0.16/0.39 funcSet: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(funcSet,definition,
% 0.16/0.39 ( funcSet
% 0.16/0.39 = ( ^ [A: $i,B: $i] :
% 0.16/0.39 ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
% 0.16/0.39 @ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(funcImageSingleton,conjecture,
% 0.16/0.39 ( setextAx
% 0.16/0.39 => ( emptysetAx
% 0.16/0.39 => ( setadjoinAx
% 0.16/0.39 => ( powersetAx
% 0.16/0.39 => ( setunionAx
% 0.16/0.39 => ( omega0Ax
% 0.16/0.39 => ( omegaSAx
% 0.16/0.39 => ( omegaIndAx
% 0.16/0.39 => ( replAx
% 0.16/0.39 => ( foundationAx
% 0.16/0.39 => ( wellorderingAx
% 0.16/0.39 => ( descrp
% 0.16/0.39 => ( dsetconstrI
% 0.16/0.39 => ( dsetconstrEL
% 0.16/0.39 => ( dsetconstrER
% 0.16/0.39 => ( exuE1
% 0.16/0.39 => ( prop2setE
% 0.16/0.39 => ( emptysetE
% 0.16/0.39 => ( emptysetimpfalse
% 0.16/0.39 => ( notinemptyset
% 0.16/0.39 => ( exuE3e
% 0.16/0.39 => ( setext
% 0.16/0.39 => ( emptyI
% 0.16/0.39 => ( noeltsimpempty
% 0.16/0.39 => ( setbeta
% 0.16/0.39 => ( nonemptyE1
% 0.16/0.39 => ( nonemptyI
% 0.16/0.39 => ( nonemptyI1
% 0.16/0.39 => ( setadjoinIL
% 0.16/0.39 => ( emptyinunitempty
% 0.16/0.39 => ( setadjoinIR
% 0.16/0.39 => ( setadjoinE
% 0.16/0.39 => ( setadjoinOr
% 0.16/0.39 => ( setoftrueEq
% 0.16/0.39 => ( powersetI
% 0.16/0.39 => ( emptyinPowerset
% 0.16/0.39 => ( emptyInPowerset
% 0.16/0.39 => ( powersetE
% 0.16/0.39 => ( setunionI
% 0.16/0.39 => ( setunionE
% 0.16/0.39 => ( subPowSU
% 0.16/0.39 => ( exuE2
% 0.16/0.39 => ( nonemptyImpWitness
% 0.16/0.39 => ( uniqinunit
% 0.16/0.39 => ( notinsingleton
% 0.16/0.39 => ( eqinunit
% 0.16/0.39 => ( singletonsswitch
% 0.16/0.39 => ( upairsetE
% 0.16/0.39 => ( upairsetIL
% 0.16/0.39 => ( upairsetIR
% 0.16/0.39 => ( emptyE1
% 0.16/0.39 => ( vacuousDall
% 0.16/0.39 => ( quantDeMorgan1
% 0.16/0.39 => ( quantDeMorgan2
% 0.16/0.39 => ( quantDeMorgan3
% 0.16/0.39 => ( quantDeMorgan4
% 0.16/0.39 => ( prop2setI
% 0.16/0.39 => ( prop2set2propI
% 0.16/0.39 => ( notdexE
% 0.16/0.39 => ( notdallE
% 0.16/0.39 => ( exuI1
% 0.16/0.39 => ( exuI3
% 0.16/0.39 => ( exuI2
% 0.16/0.39 => ( inCongP
% 0.16/0.39 => ( in__Cong
% 0.16/0.39 => ( exuE3u
% 0.16/0.39 => ( exu__Cong
% 0.16/0.39 => ( emptyset__Cong
% 0.16/0.39 => ( setadjoin__Cong
% 0.16/0.39 => ( powerset__Cong
% 0.16/0.39 => ( setunion__Cong
% 0.16/0.39 => ( omega__Cong
% 0.16/0.39 => ( exuEu
% 0.16/0.39 => ( descr__Cong
% 0.16/0.39 => ( dsetconstr__Cong
% 0.16/0.39 => ( subsetI1
% 0.16/0.39 => ( eqimpsubset2
% 0.16/0.39 => ( eqimpsubset1
% 0.16/0.39 => ( subsetI2
% 0.16/0.39 => ( emptysetsubset
% 0.16/0.39 => ( subsetE
% 0.16/0.39 => ( subsetE2
% 0.16/0.39 => ( notsubsetI
% 0.16/0.39 => ( notequalI1
% 0.16/0.39 => ( notequalI2
% 0.16/0.39 => ( subsetRefl
% 0.16/0.39 => ( subsetTrans
% 0.16/0.39 => ( setadjoinSub
% 0.16/0.39 => ( setadjoinSub2
% 0.16/0.39 => ( subset2powerset
% 0.16/0.39 => ( setextsub
% 0.16/0.39 => ( subsetemptysetimpeq
% 0.16/0.39 => ( powersetI1
% 0.16/0.39 => ( powersetE1
% 0.16/0.39 => ( inPowerset
% 0.16/0.39 => ( powersetsubset
% 0.16/0.39 => ( sepInPowerset
% 0.16/0.39 => ( sepSubset
% 0.16/0.39 => ( binunionIL
% 0.16/0.39 => ( upairset2IR
% 0.16/0.39 => ( binunionIR
% 0.16/0.39 => ( binunionEcases
% 0.16/0.39 => ( binunionE
% 0.16/0.39 => ( binunionLsub
% 0.16/0.39 => ( binunionRsub
% 0.16/0.39 => ( binintersectI
% 0.16/0.39 => ( binintersectSubset5
% 0.16/0.39 => ( binintersectEL
% 0.16/0.39 => ( binintersectLsub
% 0.16/0.39 => ( binintersectSubset2
% 0.16/0.39 => ( binintersectSubset3
% 0.16/0.39 => ( binintersectER
% 0.16/0.39 => ( disjointsetsI1
% 0.16/0.39 => ( binintersectRsub
% 0.16/0.39 => ( binintersectSubset4
% 0.16/0.39 => ( binintersectSubset1
% 0.16/0.39 => ( bs114d
% 0.16/0.39 => ( setminusI
% 0.16/0.39 => ( setminusEL
% 0.16/0.39 => ( setminusER
% 0.16/0.39 => ( setminusSubset2
% 0.16/0.39 => ( setminusERneg
% 0.16/0.39 => ( setminusELneg
% 0.16/0.39 => ( setminusILneg
% 0.16/0.39 => ( setminusIRneg
% 0.16/0.39 => ( setminusLsub
% 0.16/0.39 => ( setminusSubset1
% 0.16/0.39 => ( symdiffE
% 0.16/0.39 => ( symdiffI1
% 0.16/0.39 => ( symdiffI2
% 0.16/0.39 => ( symdiffIneg1
% 0.16/0.39 => ( symdiffIneg2
% 0.16/0.39 => ( secondinupair
% 0.16/0.39 => ( setukpairIL
% 0.16/0.39 => ( setukpairIR
% 0.16/0.39 => ( kpairiskpair
% 0.16/0.39 => ( kpairp
% 0.16/0.39 => ( singletonsubset
% 0.16/0.39 => ( singletoninpowerset
% 0.16/0.39 => ( singletoninpowunion
% 0.16/0.39 => ( upairset2E
% 0.16/0.39 => ( upairsubunion
% 0.16/0.39 => ( upairinpowunion
% 0.16/0.39 => ( ubforcartprodlem1
% 0.16/0.39 => ( ubforcartprodlem2
% 0.16/0.39 => ( ubforcartprodlem3
% 0.16/0.39 => ( cartprodpairin
% 0.16/0.39 => ( cartprodmempair1
% 0.16/0.39 => ( cartprodmempair
% 0.16/0.39 => ( setunionE2
% 0.16/0.39 => ( setunionsingleton1
% 0.16/0.39 => ( setunionsingleton2
% 0.16/0.39 => ( setunionsingleton
% 0.16/0.39 => ( singletonprop
% 0.16/0.39 => ( ex1E1
% 0.16/0.39 => ( ex1I
% 0.16/0.39 => ( ex1I2
% 0.16/0.39 => ( singletonsuniq
% 0.16/0.39 => ( setukpairinjL1
% 0.16/0.39 => ( kfstsingleton
% 0.16/0.39 => ( theprop
% 0.16/0.39 => ( kfstpairEq
% 0.16/0.39 => ( cartprodfstin
% 0.16/0.39 => ( setukpairinjL2
% 0.16/0.39 => ( setukpairinjL
% 0.16/0.39 => ( setukpairinjR11
% 0.16/0.39 => ( setukpairinjR12
% 0.16/0.39 => ( setukpairinjR1
% 0.16/0.39 => ( upairequniteq
% 0.16/0.39 => ( setukpairinjR2
% 0.16/0.39 => ( setukpairinjR
% 0.16/0.39 => ( ksndsingleton
% 0.16/0.39 => ( ksndpairEq
% 0.16/0.39 => ( kpairsurjEq
% 0.16/0.39 => ( cartprodsndin
% 0.16/0.39 => ( cartprodpairmemEL
% 0.16/0.39 => ( cartprodpairmemER
% 0.16/0.39 => ( cartprodmempaircEq
% 0.16/0.39 => ( cartprodfstpairEq
% 0.16/0.39 => ( cartprodsndpairEq
% 0.16/0.39 => ( cartprodpairsurjEq
% 0.16/0.39 => ( dpsetconstrI
% 0.16/0.39 => ( dpsetconstrSub
% 0.16/0.39 => ( setOfPairsIsBReln
% 0.16/0.39 => ( dpsetconstrERa
% 0.16/0.39 => ( dpsetconstrEL1
% 0.16/0.39 => ( dpsetconstrEL2
% 0.16/0.39 => ( dpsetconstrER
% 0.16/0.39 => ! [A: $i,B: $i,Xf: $i] :
% 0.16/0.39 ( ( func @ A @ B @ Xf )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( singleton
% 0.16/0.39 @ ( dsetconstr @ B
% 0.16/0.39 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 2.61/1.58 ---- Embedded in THF ---
% 2.61/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.61/1.58 %%% Generated on Tue Feb 24 12:30:37 EST 2026
% 2.61/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.61/1.58 %%% Logic specification used:
% 2.61/1.58 %%% thf(spec, logic, $$dhol).
% 2.61/1.58
% 2.61/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2DTF17169.p
% See solution above
% 2.61/1.58 ------------------------
% 2.84/1.62 ---- Cleaned THF ---
% 2.84/1.62 thf(in_type,type,
% 2.84/1.62 in: $i > $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(exu_type,type,
% 2.84/1.62 exu: ( $i > $o ) > $o ).
% 2.84/1.62
% 2.84/1.62 thf(exu,definition,
% 2.84/1.62 ( exu
% 2.84/1.62 = ( ^ [Xphi: $i > $o] :
% 2.84/1.62 ? [Xx: $i] :
% 2.84/1.62 ( ( Xphi @ Xx )
% 2.84/1.62 & ! [Xy: $i] :
% 2.84/1.62 ( ( Xphi @ Xy )
% 2.84/1.62 => ( Xx = Xy ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setextAx_type,type,
% 2.84/1.62 setextAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setextAx,definition,
% 2.84/1.62 ( setextAx
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 <=> ( in @ Xx @ B ) )
% 2.84/1.62 => ( A = B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptyset_type,type,
% 2.84/1.62 emptyset: $i ).
% 2.84/1.62
% 2.84/1.62 thf(emptysetAx_type,type,
% 2.84/1.62 emptysetAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptysetAx,definition,
% 2.84/1.62 ( emptysetAx
% 2.84/1.62 = ( ! [Xx: $i] :
% 2.84/1.62 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoin_type,type,
% 2.84/1.62 setadjoin: $i > $i > $i ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinAx_type,type,
% 2.84/1.62 setadjoinAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinAx,definition,
% 2.84/1.62 ( setadjoinAx
% 2.84/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.84/1.62 <=> ( ( Xy = Xx )
% 2.84/1.62 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(powerset_type,type,
% 2.84/1.62 powerset: $i > $i ).
% 2.84/1.62
% 2.84/1.62 thf(powersetAx_type,type,
% 2.84/1.62 powersetAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(powersetAx,definition,
% 2.84/1.62 ( powersetAx
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( in @ B @ ( powerset @ A ) )
% 2.84/1.62 <=> ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setunion_type,type,
% 2.84/1.62 setunion: $i > $i ).
% 2.84/1.62
% 2.84/1.62 thf(setunionAx_type,type,
% 2.84/1.62 setunionAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setunionAx,definition,
% 2.84/1.62 ( setunionAx
% 2.84/1.62 = ( ! [A: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( setunion @ A ) )
% 2.84/1.62 <=> ? [B: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 & ( in @ B @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(omega_type,type,
% 2.84/1.62 omega: $i ).
% 2.84/1.62
% 2.84/1.62 thf(omega0Ax_type,type,
% 2.84/1.62 omega0Ax: $o ).
% 2.84/1.62
% 2.84/1.62 thf(omega0Ax,definition,
% 2.84/1.62 ( omega0Ax
% 2.84/1.62 = ( in @ emptyset @ omega ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(omegaSAx_type,type,
% 2.84/1.62 omegaSAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(omegaSAx,definition,
% 2.84/1.62 ( omegaSAx
% 2.84/1.62 = ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ omega )
% 2.84/1.62 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(omegaIndAx_type,type,
% 2.84/1.62 omegaIndAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(omegaIndAx,definition,
% 2.84/1.62 ( omegaIndAx
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ( ( ( in @ emptyset @ A )
% 2.84/1.62 & ! [Xx: $i] :
% 2.84/1.62 ( ( ( in @ Xx @ omega )
% 2.84/1.62 & ( in @ Xx @ A ) )
% 2.84/1.62 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.84/1.62 => ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ omega )
% 2.84/1.62 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(replAx_type,type,
% 2.84/1.62 replAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(replAx,definition,
% 2.84/1.62 ( replAx
% 2.84/1.62 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( exu
% 2.84/1.62 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.84/1.62 => ? [B: $i] :
% 2.84/1.62 ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 <=> ? [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ A )
% 2.84/1.62 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(foundationAx_type,type,
% 2.84/1.62 foundationAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(foundationAx,definition,
% 2.84/1.62 ( foundationAx
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.84/1.62 => ? [B: $i] :
% 2.84/1.62 ( ( in @ B @ A )
% 2.84/1.62 & ~ ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(wellorderingAx_type,type,
% 2.84/1.62 wellorderingAx: $o ).
% 2.84/1.62
% 2.84/1.62 thf(wellorderingAx,definition,
% 2.84/1.62 ( wellorderingAx
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ? [B: $i] :
% 2.84/1.62 ( ! [C: $i] :
% 2.84/1.62 ( ( in @ C @ B )
% 2.84/1.62 => ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ C )
% 2.84/1.62 => ( in @ Xx @ A ) ) )
% 2.84/1.62 & ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( ( in @ Xx @ A )
% 2.84/1.62 & ( in @ Xy @ A ) )
% 2.84/1.62 => ( ! [C: $i] :
% 2.84/1.62 ( ( in @ C @ B )
% 2.84/1.62 => ( ( in @ Xx @ C )
% 2.84/1.62 <=> ( in @ Xy @ C ) ) )
% 2.84/1.62 => ( Xx = Xy ) ) )
% 2.84/1.62 & ! [C: $i,D: $i] :
% 2.84/1.62 ( ( ( in @ C @ B )
% 2.84/1.62 & ( in @ D @ B ) )
% 2.84/1.62 => ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ C )
% 2.84/1.62 => ( in @ Xx @ D ) )
% 2.84/1.62 | ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ D )
% 2.84/1.62 => ( in @ Xx @ C ) ) ) )
% 2.84/1.62 & ! [C: $i] :
% 2.84/1.62 ( ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ C )
% 2.84/1.62 => ( in @ Xx @ A ) )
% 2.84/1.62 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.84/1.62 => ? [D: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ D @ B )
% 2.84/1.62 & ( in @ Xx @ C )
% 2.84/1.62 & ~ ? [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ D )
% 2.84/1.62 & ( in @ Xy @ C ) )
% 2.84/1.62 & ! [E: $i] :
% 2.84/1.62 ( ( in @ E @ B )
% 2.84/1.62 => ( ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ E )
% 2.84/1.62 => ( in @ Xy @ D ) )
% 2.84/1.62 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(descr_type,type,
% 2.84/1.62 descr: ( $i > $o ) > $i ).
% 2.84/1.62
% 2.84/1.62 thf(descrp_type,type,
% 2.84/1.62 descrp: $o ).
% 2.84/1.62
% 2.84/1.62 thf(descrp,definition,
% 2.84/1.62 ( descrp
% 2.84/1.62 = ( ! [Xphi: $i > $o] :
% 2.84/1.62 ( ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 => ( Xphi
% 2.84/1.62 @ ( descr
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(dsetconstr_type,type,
% 2.84/1.62 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.84/1.62
% 2.84/1.62 thf(dsetconstrI_type,type,
% 2.84/1.62 dsetconstrI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(dsetconstrI,definition,
% 2.84/1.62 ( dsetconstrI
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ( Xphi @ Xx )
% 2.84/1.62 => ( in @ Xx
% 2.84/1.62 @ ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(dsetconstrEL_type,type,
% 2.84/1.62 dsetconstrEL: $o ).
% 2.84/1.62
% 2.84/1.62 thf(dsetconstrEL,definition,
% 2.84/1.62 ( dsetconstrEL
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx
% 2.84/1.62 @ ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.84/1.62 => ( in @ Xx @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(dsetconstrER_type,type,
% 2.84/1.62 dsetconstrER: $o ).
% 2.84/1.62
% 2.84/1.62 thf(dsetconstrER,definition,
% 2.84/1.62 ( dsetconstrER
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx
% 2.84/1.62 @ ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.84/1.62 => ( Xphi @ Xx ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(exuE1_type,type,
% 2.84/1.62 exuE1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(exuE1,definition,
% 2.84/1.62 ( exuE1
% 2.84/1.62 = ( ! [Xphi: $i > $o] :
% 2.84/1.62 ( ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 => ? [Xx: $i] :
% 2.84/1.62 ( ( Xphi @ Xx )
% 2.84/1.62 & ! [Xy: $i] :
% 2.84/1.62 ( ( Xphi @ Xy )
% 2.84/1.62 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(prop2set_type,type,
% 2.84/1.62 prop2set: $o > $i ).
% 2.84/1.62
% 2.84/1.62 thf(prop2setE_type,type,
% 2.84/1.62 prop2setE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(prop2setE,definition,
% 2.84/1.62 ( prop2setE
% 2.84/1.62 = ( ! [Xphi: $o,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.84/1.62 => Xphi ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptysetE_type,type,
% 2.84/1.62 emptysetE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptysetE,definition,
% 2.84/1.62 ( emptysetE
% 2.84/1.62 = ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ emptyset )
% 2.84/1.62 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptysetimpfalse_type,type,
% 2.84/1.62 emptysetimpfalse: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptysetimpfalse,definition,
% 2.84/1.62 ( emptysetimpfalse
% 2.84/1.62 = ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ emptyset )
% 2.84/1.62 => $false ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(notinemptyset_type,type,
% 2.84/1.62 notinemptyset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(notinemptyset,definition,
% 2.84/1.62 ( notinemptyset
% 2.84/1.62 = ( ! [Xx: $i] :
% 2.84/1.62 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(exuE3e_type,type,
% 2.84/1.62 exuE3e: $o ).
% 2.84/1.62
% 2.84/1.62 thf(exuE3e,definition,
% 2.84/1.62 ( exuE3e
% 2.84/1.62 = ( ! [Xphi: $i > $o] :
% 2.84/1.62 ( ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setext_type,type,
% 2.84/1.62 setext: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setext,definition,
% 2.84/1.62 ( setext
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ Xx @ B ) )
% 2.84/1.62 => ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 => ( in @ Xx @ A ) )
% 2.84/1.62 => ( A = B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptyI_type,type,
% 2.84/1.62 emptyI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptyI,definition,
% 2.84/1.62 ( emptyI
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ~ ( in @ Xx @ A )
% 2.84/1.62 => ( A = emptyset ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(noeltsimpempty_type,type,
% 2.84/1.62 noeltsimpempty: $o ).
% 2.84/1.62
% 2.84/1.62 thf(noeltsimpempty,definition,
% 2.84/1.62 ( noeltsimpempty
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ~ ( in @ Xx @ A )
% 2.84/1.62 => ( A = emptyset ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setbeta_type,type,
% 2.84/1.62 setbeta: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setbeta,definition,
% 2.84/1.62 ( setbeta
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ( in @ Xx
% 2.84/1.62 @ ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.84/1.62 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(nonempty_type,type,
% 2.84/1.62 nonempty: $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(nonempty,definition,
% 2.84/1.62 ( nonempty
% 2.84/1.62 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(nonemptyE1_type,type,
% 2.84/1.62 nonemptyE1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(nonemptyE1,definition,
% 2.84/1.62 ( nonemptyE1
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ( ( nonempty @ A )
% 2.84/1.62 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(nonemptyI_type,type,
% 2.84/1.62 nonemptyI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(nonemptyI,definition,
% 2.84/1.62 ( nonemptyI
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ( Xphi @ Xx )
% 2.84/1.62 => ( nonempty
% 2.84/1.62 @ ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(nonemptyI1_type,type,
% 2.84/1.62 nonemptyI1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(nonemptyI1,definition,
% 2.84/1.62 ( nonemptyI1
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.84/1.62 => ( nonempty @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinIL_type,type,
% 2.84/1.62 setadjoinIL: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinIL,definition,
% 2.84/1.62 ( setadjoinIL
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptyinunitempty_type,type,
% 2.84/1.62 emptyinunitempty: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptyinunitempty,definition,
% 2.84/1.62 ( emptyinunitempty
% 2.84/1.62 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinIR_type,type,
% 2.84/1.62 setadjoinIR: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinIR,definition,
% 2.84/1.62 ( setadjoinIR
% 2.84/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ A )
% 2.84/1.62 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinE_type,type,
% 2.84/1.62 setadjoinE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinE,definition,
% 2.84/1.62 ( setadjoinE
% 2.84/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.84/1.62 => ! [Xphi: $o] :
% 2.84/1.62 ( ( ( Xy = Xx )
% 2.84/1.62 => Xphi )
% 2.84/1.62 => ( ( ( in @ Xy @ A )
% 2.84/1.62 => Xphi )
% 2.84/1.62 => Xphi ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinOr_type,type,
% 2.84/1.62 setadjoinOr: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinOr,definition,
% 2.84/1.62 ( setadjoinOr
% 2.84/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.84/1.62 => ( ( Xy = Xx )
% 2.84/1.62 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setoftrueEq_type,type,
% 2.84/1.62 setoftrueEq: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setoftrueEq,definition,
% 2.84/1.62 ( setoftrueEq
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ( ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xx: $i] : $true )
% 2.84/1.62 = A ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(powersetI_type,type,
% 2.84/1.62 powersetI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(powersetI,definition,
% 2.84/1.62 ( powersetI
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 => ( in @ Xx @ A ) )
% 2.84/1.62 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptyinPowerset_type,type,
% 2.84/1.62 emptyinPowerset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptyinPowerset,definition,
% 2.84/1.62 ( emptyinPowerset
% 2.84/1.62 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptyInPowerset_type,type,
% 2.84/1.62 emptyInPowerset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptyInPowerset,definition,
% 2.84/1.62 ( emptyInPowerset
% 2.84/1.62 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(powersetE_type,type,
% 2.84/1.62 powersetE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(powersetE,definition,
% 2.84/1.62 ( powersetE
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ B @ ( powerset @ A ) )
% 2.84/1.62 => ( ( in @ Xx @ B )
% 2.84/1.62 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setunionI_type,type,
% 2.84/1.62 setunionI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setunionI,definition,
% 2.84/1.62 ( setunionI
% 2.84/1.62 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 => ( ( in @ B @ A )
% 2.84/1.62 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setunionE_type,type,
% 2.84/1.62 setunionE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setunionE,definition,
% 2.84/1.62 ( setunionE
% 2.84/1.62 = ( ! [A: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( setunion @ A ) )
% 2.84/1.62 => ! [Xphi: $o] :
% 2.84/1.62 ( ! [B: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 => ( ( in @ B @ A )
% 2.84/1.62 => Xphi ) )
% 2.84/1.62 => Xphi ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(subPowSU_type,type,
% 2.84/1.62 subPowSU: $o ).
% 2.84/1.62
% 2.84/1.62 thf(subPowSU,definition,
% 2.84/1.62 ( subPowSU
% 2.84/1.62 = ( ! [A: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(exuE2_type,type,
% 2.84/1.62 exuE2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(exuE2,definition,
% 2.84/1.62 ( exuE2
% 2.84/1.62 = ( ! [Xphi: $i > $o] :
% 2.84/1.62 ( ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 => ? [Xx: $i] :
% 2.84/1.62 ! [Xy: $i] :
% 2.84/1.62 ( ( Xphi @ Xy )
% 2.84/1.62 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(nonemptyImpWitness_type,type,
% 2.84/1.62 nonemptyImpWitness: $o ).
% 2.84/1.62
% 2.84/1.62 thf(nonemptyImpWitness,definition,
% 2.84/1.62 ( nonemptyImpWitness
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ( ( nonempty @ A )
% 2.84/1.62 => ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & $true ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(uniqinunit_type,type,
% 2.84/1.62 uniqinunit: $o ).
% 2.84/1.62
% 2.84/1.62 thf(uniqinunit,definition,
% 2.84/1.62 ( uniqinunit
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.84/1.62 => ( Xx = Xy ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(notinsingleton_type,type,
% 2.84/1.62 notinsingleton: $o ).
% 2.84/1.62
% 2.84/1.62 thf(notinsingleton,definition,
% 2.84/1.62 ( notinsingleton
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xx != Xy )
% 2.84/1.62 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(eqinunit_type,type,
% 2.84/1.62 eqinunit: $o ).
% 2.84/1.62
% 2.84/1.62 thf(eqinunit,definition,
% 2.84/1.62 ( eqinunit
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xx = Xy )
% 2.84/1.62 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(singletonsswitch_type,type,
% 2.84/1.62 singletonsswitch: $o ).
% 2.84/1.62
% 2.84/1.62 thf(singletonsswitch,definition,
% 2.84/1.62 ( singletonsswitch
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.84/1.62 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(upairsetE_type,type,
% 2.84/1.62 upairsetE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(upairsetE,definition,
% 2.84/1.62 ( upairsetE
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.84/1.62 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.84/1.62 => ( ( Xz = Xx )
% 2.84/1.62 | ( Xz = Xy ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(upairsetIL_type,type,
% 2.84/1.62 upairsetIL: $o ).
% 2.84/1.62
% 2.84/1.62 thf(upairsetIL,definition,
% 2.84/1.62 ( upairsetIL
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(upairsetIR_type,type,
% 2.84/1.62 upairsetIR: $o ).
% 2.84/1.62
% 2.84/1.62 thf(upairsetIR,definition,
% 2.84/1.62 ( upairsetIR
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptyE1_type,type,
% 2.84/1.62 emptyE1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptyE1,definition,
% 2.84/1.62 ( emptyE1
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ( Xphi @ Xx ) )
% 2.84/1.62 => ( ( ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 = emptyset )
% 2.84/1.62 => $false ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(vacuousDall_type,type,
% 2.84/1.62 vacuousDall: $o ).
% 2.84/1.62
% 2.84/1.62 thf(vacuousDall,definition,
% 2.84/1.62 ( vacuousDall
% 2.84/1.62 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ emptyset )
% 2.84/1.62 => ( Xphi @ Xx ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(quantDeMorgan1_type,type,
% 2.84/1.62 quantDeMorgan1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(quantDeMorgan1,definition,
% 2.84/1.62 ( quantDeMorgan1
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ~ ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( Xphi @ Xx ) )
% 2.84/1.62 => ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(quantDeMorgan2_type,type,
% 2.84/1.62 quantDeMorgan2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(quantDeMorgan2,definition,
% 2.84/1.62 ( quantDeMorgan2
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ~ ( Xphi @ Xx ) )
% 2.84/1.62 => ~ ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(quantDeMorgan3_type,type,
% 2.84/1.62 quantDeMorgan3: $o ).
% 2.84/1.62
% 2.84/1.62 thf(quantDeMorgan3,definition,
% 2.84/1.62 ( quantDeMorgan3
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ~ ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ( Xphi @ Xx ) )
% 2.84/1.62 => ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(quantDeMorgan4_type,type,
% 2.84/1.62 quantDeMorgan4: $o ).
% 2.84/1.62
% 2.84/1.62 thf(quantDeMorgan4,definition,
% 2.84/1.62 ( quantDeMorgan4
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ~ ( Xphi @ Xx ) )
% 2.84/1.62 => ~ ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(prop2setI_type,type,
% 2.84/1.62 prop2setI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(prop2setI,definition,
% 2.84/1.62 ( prop2setI
% 2.84/1.62 = ( ! [Xphi: $o] :
% 2.84/1.62 ( Xphi
% 2.84/1.62 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(set2prop_type,type,
% 2.84/1.62 set2prop: $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(prop2set2propI_type,type,
% 2.84/1.62 prop2set2propI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(prop2set2propI,definition,
% 2.84/1.62 ( prop2set2propI
% 2.84/1.62 = ( ! [Xphi: $o] :
% 2.84/1.62 ( Xphi
% 2.84/1.62 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(notdexE_type,type,
% 2.84/1.62 notdexE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(notdexE,definition,
% 2.84/1.62 ( notdexE
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ~ ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ( Xphi @ Xx ) )
% 2.84/1.62 => ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(notdallE_type,type,
% 2.84/1.62 notdallE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(notdallE,definition,
% 2.84/1.62 ( notdallE
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ~ ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( Xphi @ Xx ) )
% 2.84/1.62 => ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(exuI1_type,type,
% 2.84/1.62 exuI1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(exuI1,definition,
% 2.84/1.62 ( exuI1
% 2.84/1.62 = ( ! [Xphi: $i > $o] :
% 2.84/1.62 ( ? [Xx: $i] :
% 2.84/1.62 ( ( Xphi @ Xx )
% 2.84/1.62 & ! [Xy: $i] :
% 2.84/1.62 ( ( Xphi @ Xy )
% 2.84/1.62 => ( Xx = Xy ) ) )
% 2.84/1.62 => ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(exuI3_type,type,
% 2.84/1.62 exuI3: $o ).
% 2.84/1.62
% 2.84/1.62 thf(exuI3,definition,
% 2.84/1.62 ( exuI3
% 2.84/1.62 = ( ! [Xphi: $i > $o] :
% 2.84/1.62 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.84/1.62 => ( ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xphi @ Xx )
% 2.84/1.62 => ( ( Xphi @ Xy )
% 2.84/1.62 => ( Xx = Xy ) ) )
% 2.84/1.62 => ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(exuI2_type,type,
% 2.84/1.62 exuI2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(exuI2,definition,
% 2.84/1.62 ( exuI2
% 2.84/1.62 = ( ! [Xphi: $i > $o] :
% 2.84/1.62 ( ? [Xx: $i] :
% 2.84/1.62 ! [Xy: $i] :
% 2.84/1.62 ( ( Xphi @ Xy )
% 2.84/1.62 <=> ( Xy = Xx ) )
% 2.84/1.62 => ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(inCongP_type,type,
% 2.84/1.62 inCongP: $o ).
% 2.84/1.62
% 2.84/1.62 thf(inCongP,definition,
% 2.84/1.62 ( inCongP
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( A = B )
% 2.84/1.62 => ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xx = Xy )
% 2.84/1.62 => ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(in__Cong_type,type,
% 2.84/1.62 in__Cong: $o ).
% 2.84/1.62
% 2.84/1.62 thf(in__Cong,definition,
% 2.84/1.62 ( in__Cong
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( A = B )
% 2.84/1.62 => ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xx = Xy )
% 2.84/1.62 => ( ( in @ Xx @ A )
% 2.84/1.62 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(exuE3u_type,type,
% 2.84/1.62 exuE3u: $o ).
% 2.84/1.62
% 2.84/1.62 thf(exuE3u,definition,
% 2.84/1.62 ( exuE3u
% 2.84/1.62 = ( ! [Xphi: $i > $o] :
% 2.84/1.62 ( ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 => ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xphi @ Xx )
% 2.84/1.62 => ( ( Xphi @ Xy )
% 2.84/1.62 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(exu__Cong_type,type,
% 2.84/1.62 exu__Cong: $o ).
% 2.84/1.62
% 2.84/1.62 thf(exu__Cong,definition,
% 2.84/1.62 ( exu__Cong
% 2.84/1.62 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.84/1.62 ( ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xx = Xy )
% 2.84/1.62 => ( ( Xphi @ Xx )
% 2.84/1.62 <=> ( Xpsi @ Xy ) ) )
% 2.84/1.62 => ( ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 <=> ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptyset__Cong_type,type,
% 2.84/1.62 emptyset__Cong: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptyset__Cong,definition,
% 2.84/1.62 ( emptyset__Cong
% 2.84/1.62 = ( emptyset = emptyset ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoin__Cong_type,type,
% 2.84/1.62 setadjoin__Cong: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoin__Cong,definition,
% 2.84/1.62 ( setadjoin__Cong
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xx = Xy )
% 2.84/1.62 => ! [Xz: $i,Xu: $i] :
% 2.84/1.62 ( ( Xz = Xu )
% 2.84/1.62 => ( ( setadjoin @ Xx @ Xz )
% 2.84/1.62 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(powerset__Cong_type,type,
% 2.84/1.62 powerset__Cong: $o ).
% 2.84/1.62
% 2.84/1.62 thf(powerset__Cong,definition,
% 2.84/1.62 ( powerset__Cong
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( A = B )
% 2.84/1.62 => ( ( powerset @ A )
% 2.84/1.62 = ( powerset @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setunion__Cong_type,type,
% 2.84/1.62 setunion__Cong: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setunion__Cong,definition,
% 2.84/1.62 ( setunion__Cong
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( A = B )
% 2.84/1.62 => ( ( setunion @ A )
% 2.84/1.62 = ( setunion @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(omega__Cong_type,type,
% 2.84/1.62 omega__Cong: $o ).
% 2.84/1.62
% 2.84/1.62 thf(omega__Cong,definition,
% 2.84/1.62 ( omega__Cong
% 2.84/1.62 = ( omega = omega ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(exuEu_type,type,
% 2.84/1.62 exuEu: $o ).
% 2.84/1.62
% 2.84/1.62 thf(exuEu,definition,
% 2.84/1.62 ( exuEu
% 2.84/1.62 = ( ! [Xphi: $i > $o] :
% 2.84/1.62 ( ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 => ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xphi @ Xx )
% 2.84/1.62 => ( ( Xphi @ Xy )
% 2.84/1.62 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(descr__Cong_type,type,
% 2.84/1.62 descr__Cong: $o ).
% 2.84/1.62
% 2.84/1.62 thf(descr__Cong,definition,
% 2.84/1.62 ( descr__Cong
% 2.84/1.62 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.84/1.62 ( ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( Xx = Xy )
% 2.84/1.62 => ( ( Xphi @ Xx )
% 2.84/1.62 <=> ( Xpsi @ Xy ) ) )
% 2.84/1.62 => ( ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 => ( ( exu
% 2.84/1.62 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.84/1.62 => ( ( descr
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 = ( descr
% 2.84/1.62 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(dsetconstr__Cong_type,type,
% 2.84/1.62 dsetconstr__Cong: $o ).
% 2.84/1.62
% 2.84/1.62 thf(dsetconstr__Cong,definition,
% 2.84/1.62 ( dsetconstr__Cong
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( A = B )
% 2.84/1.62 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ B )
% 2.84/1.62 => ( ( Xx = Xy )
% 2.84/1.62 => ( ( Xphi @ Xx )
% 2.84/1.62 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.84/1.62 => ( ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 = ( dsetconstr @ B
% 2.84/1.62 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(subset_type,type,
% 2.84/1.62 subset: $i > $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(disjoint_type,type,
% 2.84/1.62 disjoint: $i > $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(setsmeet_type,type,
% 2.84/1.62 setsmeet: $i > $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(subsetI1_type,type,
% 2.84/1.62 subsetI1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(subsetI1,definition,
% 2.84/1.62 ( subsetI1
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ Xx @ B ) )
% 2.84/1.62 => ( subset @ A @ B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(eqimpsubset2_type,type,
% 2.84/1.62 eqimpsubset2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(eqimpsubset2,definition,
% 2.84/1.62 ( eqimpsubset2
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( A = B )
% 2.84/1.62 => ( subset @ B @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(eqimpsubset1_type,type,
% 2.84/1.62 eqimpsubset1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(eqimpsubset1,definition,
% 2.84/1.62 ( eqimpsubset1
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( A = B )
% 2.84/1.62 => ( subset @ A @ B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(subsetI2_type,type,
% 2.84/1.62 subsetI2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(subsetI2,definition,
% 2.84/1.62 ( subsetI2
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ Xx @ B ) )
% 2.84/1.62 => ( subset @ A @ B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(emptysetsubset_type,type,
% 2.84/1.62 emptysetsubset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(emptysetsubset,definition,
% 2.84/1.62 ( emptysetsubset
% 2.84/1.62 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(subsetE_type,type,
% 2.84/1.62 subsetE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(subsetE,definition,
% 2.84/1.62 ( subsetE
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( subset @ A @ B )
% 2.84/1.62 => ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(subsetE2_type,type,
% 2.84/1.62 subsetE2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(subsetE2,definition,
% 2.84/1.62 ( subsetE2
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( subset @ A @ B )
% 2.84/1.62 => ( ~ ( in @ Xx @ B )
% 2.84/1.62 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(notsubsetI_type,type,
% 2.84/1.62 notsubsetI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(notsubsetI,definition,
% 2.84/1.62 ( notsubsetI
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ~ ( in @ Xx @ B )
% 2.84/1.62 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(notequalI1_type,type,
% 2.84/1.62 notequalI1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(notequalI1,definition,
% 2.84/1.62 ( notequalI1
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ~ ( subset @ A @ B )
% 2.84/1.62 => ( A != B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(notequalI2_type,type,
% 2.84/1.62 notequalI2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(notequalI2,definition,
% 2.84/1.62 ( notequalI2
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ~ ( in @ Xx @ B )
% 2.84/1.62 => ( A != B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(subsetRefl_type,type,
% 2.84/1.62 subsetRefl: $o ).
% 2.84/1.62
% 2.84/1.62 thf(subsetRefl,definition,
% 2.84/1.62 ( subsetRefl
% 2.84/1.62 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(subsetTrans_type,type,
% 2.84/1.62 subsetTrans: $o ).
% 2.84/1.62
% 2.84/1.62 thf(subsetTrans,definition,
% 2.84/1.62 ( subsetTrans
% 2.84/1.62 = ( ! [A: $i,B: $i,C: $i] :
% 2.84/1.62 ( ( subset @ A @ B )
% 2.84/1.62 => ( ( subset @ B @ C )
% 2.84/1.62 => ( subset @ A @ C ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinSub_type,type,
% 2.84/1.62 setadjoinSub: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinSub,definition,
% 2.84/1.62 ( setadjoinSub
% 2.84/1.62 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinSub2_type,type,
% 2.84/1.62 setadjoinSub2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setadjoinSub2,definition,
% 2.84/1.62 ( setadjoinSub2
% 2.84/1.62 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.84/1.62 ( ( subset @ A @ B )
% 2.84/1.62 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(subset2powerset_type,type,
% 2.84/1.62 subset2powerset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(subset2powerset,definition,
% 2.84/1.62 ( subset2powerset
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( subset @ A @ B )
% 2.84/1.62 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setextsub_type,type,
% 2.84/1.62 setextsub: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setextsub,definition,
% 2.84/1.62 ( setextsub
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( subset @ A @ B )
% 2.84/1.62 => ( ( subset @ B @ A )
% 2.84/1.62 => ( A = B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(subsetemptysetimpeq_type,type,
% 2.84/1.62 subsetemptysetimpeq: $o ).
% 2.84/1.62
% 2.84/1.62 thf(subsetemptysetimpeq,definition,
% 2.84/1.62 ( subsetemptysetimpeq
% 2.84/1.62 = ( ! [A: $i] :
% 2.84/1.62 ( ( subset @ A @ emptyset )
% 2.84/1.62 => ( A = emptyset ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(powersetI1_type,type,
% 2.84/1.62 powersetI1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(powersetI1,definition,
% 2.84/1.62 ( powersetI1
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( subset @ B @ A )
% 2.84/1.62 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(powersetE1_type,type,
% 2.84/1.62 powersetE1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(powersetE1,definition,
% 2.84/1.62 ( powersetE1
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( in @ B @ ( powerset @ A ) )
% 2.84/1.62 => ( subset @ B @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(inPowerset_type,type,
% 2.84/1.62 inPowerset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(inPowerset,definition,
% 2.84/1.62 ( inPowerset
% 2.84/1.62 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(powersetsubset_type,type,
% 2.84/1.62 powersetsubset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(powersetsubset,definition,
% 2.84/1.62 ( powersetsubset
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( subset @ A @ B )
% 2.84/1.62 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(sepInPowerset_type,type,
% 2.84/1.62 sepInPowerset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(sepInPowerset,definition,
% 2.84/1.62 ( sepInPowerset
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( in
% 2.84/1.62 @ ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 @ ( powerset @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(sepSubset_type,type,
% 2.84/1.62 sepSubset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(sepSubset,definition,
% 2.84/1.62 ( sepSubset
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( subset
% 2.84/1.62 @ ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 @ A ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binunion_type,type,
% 2.84/1.62 binunion: $i > $i > $i ).
% 2.84/1.62
% 2.84/1.62 thf(binunionIL_type,type,
% 2.84/1.62 binunionIL: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binunionIL,definition,
% 2.84/1.62 ( binunionIL
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(upairset2IR_type,type,
% 2.84/1.62 upairset2IR: $o ).
% 2.84/1.62
% 2.84/1.62 thf(upairset2IR,definition,
% 2.84/1.62 ( upairset2IR
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binunionIR_type,type,
% 2.84/1.62 binunionIR: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binunionIR,definition,
% 2.84/1.62 ( binunionIR
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binunionEcases_type,type,
% 2.84/1.62 binunionEcases: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binunionEcases,definition,
% 2.84/1.62 ( binunionEcases
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.84/1.62 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.84/1.62 => ( ( ( in @ Xx @ A )
% 2.84/1.62 => Xphi )
% 2.84/1.62 => ( ( ( in @ Xx @ B )
% 2.84/1.62 => Xphi )
% 2.84/1.62 => Xphi ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binunionE_type,type,
% 2.84/1.62 binunionE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binunionE,definition,
% 2.84/1.62 ( binunionE
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.84/1.62 => ( ( in @ Xx @ A )
% 2.84/1.62 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binunionLsub_type,type,
% 2.84/1.62 binunionLsub: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binunionLsub,definition,
% 2.84/1.62 ( binunionLsub
% 2.84/1.62 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binunionRsub_type,type,
% 2.84/1.62 binunionRsub: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binunionRsub,definition,
% 2.84/1.62 ( binunionRsub
% 2.84/1.62 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersect_type,type,
% 2.84/1.62 binintersect: $i > $i > $i ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectI_type,type,
% 2.84/1.62 binintersectI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectI,definition,
% 2.84/1.62 ( binintersectI
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ( in @ Xx @ B )
% 2.84/1.62 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset5_type,type,
% 2.84/1.62 binintersectSubset5: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset5,definition,
% 2.84/1.62 ( binintersectSubset5
% 2.84/1.62 = ( ! [A: $i,B: $i,C: $i] :
% 2.84/1.62 ( ( subset @ C @ A )
% 2.84/1.62 => ( ( subset @ C @ B )
% 2.84/1.62 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectEL_type,type,
% 2.84/1.62 binintersectEL: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectEL,definition,
% 2.84/1.62 ( binintersectEL
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.84/1.62 => ( in @ Xx @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectLsub_type,type,
% 2.84/1.62 binintersectLsub: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectLsub,definition,
% 2.84/1.62 ( binintersectLsub
% 2.84/1.62 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset2_type,type,
% 2.84/1.62 binintersectSubset2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset2,definition,
% 2.84/1.62 ( binintersectSubset2
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( subset @ A @ B )
% 2.84/1.62 => ( ( binintersect @ A @ B )
% 2.84/1.62 = A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset3_type,type,
% 2.84/1.62 binintersectSubset3: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset3,definition,
% 2.84/1.62 ( binintersectSubset3
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( ( binintersect @ A @ B )
% 2.84/1.62 = B )
% 2.84/1.62 => ( subset @ B @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectER_type,type,
% 2.84/1.62 binintersectER: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectER,definition,
% 2.84/1.62 ( binintersectER
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.84/1.62 => ( in @ Xx @ B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(disjointsetsI1_type,type,
% 2.84/1.62 disjointsetsI1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(disjointsetsI1,definition,
% 2.84/1.62 ( disjointsetsI1
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ~ ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ( in @ Xx @ B ) )
% 2.84/1.62 => ( ( binintersect @ A @ B )
% 2.84/1.62 = emptyset ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectRsub_type,type,
% 2.84/1.62 binintersectRsub: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectRsub,definition,
% 2.84/1.62 ( binintersectRsub
% 2.84/1.62 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset4_type,type,
% 2.84/1.62 binintersectSubset4: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset4,definition,
% 2.84/1.62 ( binintersectSubset4
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( subset @ B @ A )
% 2.84/1.62 => ( ( binintersect @ A @ B )
% 2.84/1.62 = B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset1_type,type,
% 2.84/1.62 binintersectSubset1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(binintersectSubset1,definition,
% 2.84/1.62 ( binintersectSubset1
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( ( binintersect @ A @ B )
% 2.84/1.62 = A )
% 2.84/1.62 => ( subset @ A @ B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(bs114d_type,type,
% 2.84/1.62 bs114d: $o ).
% 2.84/1.62
% 2.84/1.62 thf(bs114d,definition,
% 2.84/1.62 ( bs114d
% 2.84/1.62 = ( ! [A: $i,B: $i,C: $i] :
% 2.84/1.62 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.84/1.62 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(regular_type,type,
% 2.84/1.62 regular: $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminus_type,type,
% 2.84/1.62 setminus: $i > $i > $i ).
% 2.84/1.62
% 2.84/1.62 thf(setminusI_type,type,
% 2.84/1.62 setminusI: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusI,definition,
% 2.84/1.62 ( setminusI
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ~ ( in @ Xx @ B )
% 2.84/1.62 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setminusEL_type,type,
% 2.84/1.62 setminusEL: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusEL,definition,
% 2.84/1.62 ( setminusEL
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.84/1.62 => ( in @ Xx @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setminusER_type,type,
% 2.84/1.62 setminusER: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusER,definition,
% 2.84/1.62 ( setminusER
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.84/1.62 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setminusSubset2_type,type,
% 2.84/1.62 setminusSubset2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusSubset2,definition,
% 2.84/1.62 ( setminusSubset2
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( subset @ A @ B )
% 2.84/1.62 => ( ( setminus @ A @ B )
% 2.84/1.62 = emptyset ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setminusERneg_type,type,
% 2.84/1.62 setminusERneg: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusERneg,definition,
% 2.84/1.62 ( setminusERneg
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.84/1.62 => ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setminusELneg_type,type,
% 2.84/1.62 setminusELneg: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusELneg,definition,
% 2.84/1.62 ( setminusELneg
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.84/1.62 => ( ~ ( in @ Xx @ B )
% 2.84/1.62 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setminusILneg_type,type,
% 2.84/1.62 setminusILneg: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusILneg,definition,
% 2.84/1.62 ( setminusILneg
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ~ ( in @ Xx @ A )
% 2.84/1.62 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setminusIRneg_type,type,
% 2.84/1.62 setminusIRneg: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusIRneg,definition,
% 2.84/1.62 ( setminusIRneg
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ B )
% 2.84/1.62 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setminusLsub_type,type,
% 2.84/1.62 setminusLsub: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusLsub,definition,
% 2.84/1.62 ( setminusLsub
% 2.84/1.62 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setminusSubset1_type,type,
% 2.84/1.62 setminusSubset1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setminusSubset1,definition,
% 2.84/1.62 ( setminusSubset1
% 2.84/1.62 = ( ! [A: $i,B: $i] :
% 2.84/1.62 ( ( ( setminus @ A @ B )
% 2.84/1.62 = emptyset )
% 2.84/1.62 => ( subset @ A @ B ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(symdiff_type,type,
% 2.84/1.62 symdiff: $i > $i > $i ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffE_type,type,
% 2.84/1.62 symdiffE: $o ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffE,definition,
% 2.84/1.62 ( symdiffE
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.84/1.62 => ! [Xphi: $o] :
% 2.84/1.62 ( ( ( in @ Xx @ A )
% 2.84/1.62 => ( ~ ( in @ Xx @ B )
% 2.84/1.62 => Xphi ) )
% 2.84/1.62 => ( ( ~ ( in @ Xx @ A )
% 2.84/1.62 => ( ( in @ Xx @ B )
% 2.84/1.62 => Xphi ) )
% 2.84/1.62 => Xphi ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffI1_type,type,
% 2.84/1.62 symdiffI1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffI1,definition,
% 2.84/1.62 ( symdiffI1
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ~ ( in @ Xx @ B )
% 2.84/1.62 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffI2_type,type,
% 2.84/1.62 symdiffI2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffI2,definition,
% 2.84/1.62 ( symdiffI2
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ~ ( in @ Xx @ A )
% 2.84/1.62 => ( ( in @ Xx @ B )
% 2.84/1.62 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffIneg1_type,type,
% 2.84/1.62 symdiffIneg1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffIneg1,definition,
% 2.84/1.62 ( symdiffIneg1
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ( in @ Xx @ B )
% 2.84/1.62 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffIneg2_type,type,
% 2.84/1.62 symdiffIneg2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(symdiffIneg2,definition,
% 2.84/1.62 ( symdiffIneg2
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ~ ( in @ Xx @ A )
% 2.84/1.62 => ( ~ ( in @ Xx @ B )
% 2.84/1.62 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(iskpair_type,type,
% 2.84/1.62 iskpair: $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(secondinupair_type,type,
% 2.84/1.62 secondinupair: $o ).
% 2.84/1.62
% 2.84/1.62 thf(secondinupair,definition,
% 2.84/1.62 ( secondinupair
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setukpairIL_type,type,
% 2.84/1.62 setukpairIL: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setukpairIL,definition,
% 2.84/1.62 ( setukpairIL
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setukpairIR_type,type,
% 2.84/1.62 setukpairIR: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setukpairIR,definition,
% 2.84/1.62 ( setukpairIR
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(kpairiskpair_type,type,
% 2.84/1.62 kpairiskpair: $o ).
% 2.84/1.62
% 2.84/1.62 thf(kpairiskpair,definition,
% 2.84/1.62 ( kpairiskpair
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(kpair_type,type,
% 2.84/1.62 kpair: $i > $i > $i ).
% 2.84/1.62
% 2.84/1.62 thf(kpairp_type,type,
% 2.84/1.62 kpairp: $o ).
% 2.84/1.62
% 2.84/1.62 thf(kpairp,definition,
% 2.84/1.62 ( kpairp
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(cartprod_type,type,
% 2.84/1.62 cartprod: $i > $i > $i ).
% 2.84/1.62
% 2.84/1.62 thf(singletonsubset_type,type,
% 2.84/1.62 singletonsubset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(singletonsubset,definition,
% 2.84/1.62 ( singletonsubset
% 2.84/1.62 = ( ! [A: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(singletoninpowerset_type,type,
% 2.84/1.62 singletoninpowerset: $o ).
% 2.84/1.62
% 2.84/1.62 thf(singletoninpowerset,definition,
% 2.84/1.62 ( singletoninpowerset
% 2.84/1.62 = ( ! [A: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(singletoninpowunion_type,type,
% 2.84/1.62 singletoninpowunion: $o ).
% 2.84/1.62
% 2.84/1.62 thf(singletoninpowunion,definition,
% 2.84/1.62 ( singletoninpowunion
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(upairset2E_type,type,
% 2.84/1.62 upairset2E: $o ).
% 2.84/1.62
% 2.84/1.62 thf(upairset2E,definition,
% 2.84/1.62 ( upairset2E
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.84/1.62 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.84/1.62 => ( ( Xz = Xx )
% 2.84/1.62 | ( Xz = Xy ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(upairsubunion_type,type,
% 2.84/1.62 upairsubunion: $o ).
% 2.84/1.62
% 2.84/1.62 thf(upairsubunion,definition,
% 2.84/1.62 ( upairsubunion
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ B )
% 2.84/1.62 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(upairinpowunion_type,type,
% 2.84/1.62 upairinpowunion: $o ).
% 2.84/1.62
% 2.84/1.62 thf(upairinpowunion,definition,
% 2.84/1.62 ( upairinpowunion
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ B )
% 2.84/1.62 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(ubforcartprodlem1_type,type,
% 2.84/1.62 ubforcartprodlem1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(ubforcartprodlem1,definition,
% 2.84/1.62 ( ubforcartprodlem1
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ B )
% 2.84/1.62 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(ubforcartprodlem2_type,type,
% 2.84/1.62 ubforcartprodlem2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(ubforcartprodlem2,definition,
% 2.84/1.62 ( ubforcartprodlem2
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ B )
% 2.84/1.62 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(ubforcartprodlem3_type,type,
% 2.84/1.62 ubforcartprodlem3: $o ).
% 2.84/1.62
% 2.84/1.62 thf(ubforcartprodlem3,definition,
% 2.84/1.62 ( ubforcartprodlem3
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ B )
% 2.84/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(cartprodpairin_type,type,
% 2.84/1.62 cartprodpairin: $o ).
% 2.84/1.62
% 2.84/1.62 thf(cartprodpairin,definition,
% 2.84/1.62 ( cartprodpairin
% 2.84/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ B )
% 2.84/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(cartprodmempair1_type,type,
% 2.84/1.62 cartprodmempair1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(cartprodmempair1,definition,
% 2.84/1.62 ( cartprodmempair1
% 2.84/1.62 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.84/1.62 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.84/1.62 => ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ? [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ B )
% 2.84/1.62 & ( Xu
% 2.84/1.62 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(cartprodmempair_type,type,
% 2.84/1.62 cartprodmempair: $o ).
% 2.84/1.62
% 2.84/1.62 thf(cartprodmempair,definition,
% 2.84/1.62 ( cartprodmempair
% 2.84/1.62 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.84/1.62 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.84/1.62 => ( iskpair @ Xu ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setunionE2_type,type,
% 2.84/1.62 setunionE2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setunionE2,definition,
% 2.84/1.62 ( setunionE2
% 2.84/1.62 = ( ! [A: $i,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ ( setunion @ A ) )
% 2.84/1.62 => ? [X: $i] :
% 2.84/1.62 ( ( in @ X @ A )
% 2.84/1.62 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setunionsingleton1_type,type,
% 2.84/1.62 setunionsingleton1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setunionsingleton1,definition,
% 2.84/1.62 ( setunionsingleton1
% 2.84/1.62 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setunionsingleton2_type,type,
% 2.84/1.62 setunionsingleton2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setunionsingleton2,definition,
% 2.84/1.62 ( setunionsingleton2
% 2.84/1.62 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(setunionsingleton_type,type,
% 2.84/1.62 setunionsingleton: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setunionsingleton,definition,
% 2.84/1.62 ( setunionsingleton
% 2.84/1.62 = ( ! [Xx: $i] :
% 2.84/1.62 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.84/1.62 = Xx ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(singleton_type,type,
% 2.84/1.62 singleton: $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(singleton,definition,
% 2.84/1.62 ( singleton
% 2.84/1.62 = ( ^ [A: $i] :
% 2.84/1.62 ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ( A
% 2.84/1.62 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(singletonprop_type,type,
% 2.84/1.62 singletonprop: $o ).
% 2.84/1.62
% 2.84/1.62 thf(singletonprop,definition,
% 2.84/1.62 ( singletonprop
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ A )
% 2.84/1.62 => ( ( Xphi @ Xx )
% 2.84/1.62 => ( ( Xphi @ Xy )
% 2.84/1.62 => ( Xx = Xy ) ) ) ) )
% 2.84/1.62 => ( ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ( Xphi @ Xx ) )
% 2.84/1.62 => ( singleton
% 2.84/1.62 @ ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(ex1_type,type,
% 2.84/1.62 ex1: $i > ( $i > $o ) > $o ).
% 2.84/1.62
% 2.84/1.62 thf(ex1,definition,
% 2.84/1.62 ( ex1
% 2.84/1.62 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( singleton
% 2.84/1.62 @ ( dsetconstr @ A
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(ex1E1_type,type,
% 2.84/1.62 ex1E1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(ex1E1,definition,
% 2.84/1.62 ( ex1E1
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ( ex1 @ A
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.84/1.62 => ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(ex1I_type,type,
% 2.84/1.62 ex1I: $o ).
% 2.84/1.62
% 2.84/1.62 thf(ex1I,definition,
% 2.84/1.62 ( ex1I
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ( ( Xphi @ Xx )
% 2.84/1.62 => ( ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ A )
% 2.84/1.62 => ( ( Xphi @ Xy )
% 2.84/1.62 => ( Xy = Xx ) ) )
% 2.84/1.62 => ( ex1 @ A
% 2.84/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(ex1I2_type,type,
% 2.84/1.62 ex1I2: $o ).
% 2.84/1.62
% 2.84/1.62 thf(ex1I2,definition,
% 2.84/1.62 ( ex1I2
% 2.84/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.84/1.62 ( ! [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 => ! [Xy: $i] :
% 2.84/1.62 ( ( in @ Xy @ A )
% 2.84/1.62 => ( ( Xphi @ Xx )
% 2.84/1.62 => ( ( Xphi @ Xy )
% 2.84/1.62 => ( Xx = Xy ) ) ) ) )
% 2.84/1.62 => ( ? [Xx: $i] :
% 2.84/1.62 ( ( in @ Xx @ A )
% 2.84/1.62 & ( Xphi @ Xx ) )
% 2.84/1.62 => ( ex1 @ A
% 2.84/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(singletonsuniq_type,type,
% 2.84/1.62 singletonsuniq: $o ).
% 2.84/1.62
% 2.84/1.62 thf(singletonsuniq,definition,
% 2.84/1.62 ( singletonsuniq
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.62 ( ( ( setadjoin @ Xx @ emptyset )
% 2.84/1.62 = ( setadjoin @ Xy @ emptyset ) )
% 2.84/1.62 => ( Xx = Xy ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(atmost1p_type,type,
% 2.84/1.62 atmost1p: $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(atleast2p_type,type,
% 2.84/1.62 atleast2p: $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(atmost2p_type,type,
% 2.84/1.62 atmost2p: $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(upairsetp_type,type,
% 2.84/1.62 upairsetp: $i > $o ).
% 2.84/1.62
% 2.84/1.62 thf(setukpairinjL1_type,type,
% 2.84/1.62 setukpairinjL1: $o ).
% 2.84/1.62
% 2.84/1.62 thf(setukpairinjL1,definition,
% 2.84/1.62 ( setukpairinjL1
% 2.84/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.84/1.62 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.84/1.62 => ( Xx = Xz ) ) ) ) ).
% 2.84/1.62
% 2.84/1.62 thf(kfstsingleton_type,type,
% 2.84/1.62 kfstsingleton: $o ).
% 2.84/1.63
% 2.84/1.63 thf(kfstsingleton,definition,
% 2.84/1.63 ( kfstsingleton
% 2.84/1.63 = ( ! [Xu: $i] :
% 2.84/1.63 ( ( iskpair @ Xu )
% 2.84/1.63 => ( singleton
% 2.84/1.63 @ ( dsetconstr @ ( setunion @ Xu )
% 2.84/1.63 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(theprop_type,type,
% 2.84/1.63 theprop: $o ).
% 2.84/1.63
% 2.84/1.63 thf(theprop,definition,
% 2.84/1.63 ( theprop
% 2.84/1.63 = ( ! [X: $i] :
% 2.84/1.63 ( ( singleton @ X )
% 2.84/1.63 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(kfst_type,type,
% 2.84/1.63 kfst: $i > $i ).
% 2.84/1.63
% 2.84/1.63 thf(kfstpairEq_type,type,
% 2.84/1.63 kfstpairEq: $o ).
% 2.84/1.63
% 2.84/1.63 thf(kfstpairEq,definition,
% 2.84/1.63 ( kfstpairEq
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.63 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.84/1.63 = Xx ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodfstin_type,type,
% 2.84/1.63 cartprodfstin: $o ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodfstin,definition,
% 2.84/1.63 ( cartprodfstin
% 2.84/1.63 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.84/1.63 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.84/1.63 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjL2_type,type,
% 2.84/1.63 setukpairinjL2: $o ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjL2,definition,
% 2.84/1.63 ( setukpairinjL2
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.84/1.63 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.84/1.63 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.84/1.63 => ( Xx = Xz ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjL_type,type,
% 2.84/1.63 setukpairinjL: $o ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjL,definition,
% 2.84/1.63 ( setukpairinjL
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.84/1.63 ( ( ( kpair @ Xx @ Xy )
% 2.84/1.63 = ( kpair @ Xz @ Xu ) )
% 2.84/1.63 => ( Xx = Xz ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR11_type,type,
% 2.84/1.63 setukpairinjR11: $o ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR11,definition,
% 2.84/1.63 ( setukpairinjR11
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.63 ( ( Xx = Xy )
% 2.84/1.63 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.84/1.63 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR12_type,type,
% 2.84/1.63 setukpairinjR12: $o ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR12,definition,
% 2.84/1.63 ( setukpairinjR12
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.63 ( ( Xx = Xy )
% 2.84/1.63 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.84/1.63 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR1_type,type,
% 2.84/1.63 setukpairinjR1: $o ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR1,definition,
% 2.84/1.63 ( setukpairinjR1
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.84/1.63 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.84/1.63 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.84/1.63 => ( ( Xz = Xu )
% 2.84/1.63 => ( Xy = Xu ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(upairequniteq_type,type,
% 2.84/1.63 upairequniteq: $o ).
% 2.84/1.63
% 2.84/1.63 thf(upairequniteq,definition,
% 2.84/1.63 ( upairequniteq
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.84/1.63 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.84/1.63 = ( setadjoin @ Xz @ emptyset ) )
% 2.84/1.63 => ( Xx = Xy ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR2_type,type,
% 2.84/1.63 setukpairinjR2: $o ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR2,definition,
% 2.84/1.63 ( setukpairinjR2
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.84/1.63 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.84/1.63 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.84/1.63 => ( Xy = Xu ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR_type,type,
% 2.84/1.63 setukpairinjR: $o ).
% 2.84/1.63
% 2.84/1.63 thf(setukpairinjR,definition,
% 2.84/1.63 ( setukpairinjR
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.84/1.63 ( ( ( kpair @ Xx @ Xy )
% 2.84/1.63 = ( kpair @ Xz @ Xu ) )
% 2.84/1.63 => ( Xy = Xu ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(ksndsingleton_type,type,
% 2.84/1.63 ksndsingleton: $o ).
% 2.84/1.63
% 2.84/1.63 thf(ksndsingleton,definition,
% 2.84/1.63 ( ksndsingleton
% 2.84/1.63 = ( ! [Xu: $i] :
% 2.84/1.63 ( ( iskpair @ Xu )
% 2.84/1.63 => ( singleton
% 2.84/1.63 @ ( dsetconstr @ ( setunion @ Xu )
% 2.84/1.63 @ ^ [Xx: $i] :
% 2.84/1.63 ( Xu
% 2.84/1.63 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(ksnd_type,type,
% 2.84/1.63 ksnd: $i > $i ).
% 2.84/1.63
% 2.84/1.63 thf(ksndpairEq_type,type,
% 2.84/1.63 ksndpairEq: $o ).
% 2.84/1.63
% 2.84/1.63 thf(ksndpairEq,definition,
% 2.84/1.63 ( ksndpairEq
% 2.84/1.63 = ( ! [Xx: $i,Xy: $i] :
% 2.84/1.63 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.84/1.63 = Xy ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(kpairsurjEq_type,type,
% 2.84/1.63 kpairsurjEq: $o ).
% 2.84/1.63
% 2.84/1.63 thf(kpairsurjEq,definition,
% 2.84/1.63 ( kpairsurjEq
% 2.84/1.63 = ( ! [Xu: $i] :
% 2.84/1.63 ( ( iskpair @ Xu )
% 2.84/1.63 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.84/1.63 = Xu ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodsndin_type,type,
% 2.84/1.63 cartprodsndin: $o ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodsndin,definition,
% 2.84/1.63 ( cartprodsndin
% 2.84/1.63 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.84/1.63 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.84/1.63 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodpairmemEL_type,type,
% 2.84/1.63 cartprodpairmemEL: $o ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodpairmemEL,definition,
% 2.84/1.63 ( cartprodpairmemEL
% 2.84/1.63 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.84/1.63 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.84/1.63 => ( in @ Xx @ A ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodpairmemER_type,type,
% 2.84/1.63 cartprodpairmemER: $o ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodpairmemER,definition,
% 2.84/1.63 ( cartprodpairmemER
% 2.84/1.63 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.84/1.63 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.84/1.63 => ( in @ Xy @ B ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodmempaircEq_type,type,
% 2.84/1.63 cartprodmempaircEq: $o ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodmempaircEq,definition,
% 2.84/1.63 ( cartprodmempaircEq
% 2.84/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.63 ( ( in @ Xx @ A )
% 2.84/1.63 => ! [Xy: $i] :
% 2.84/1.63 ( ( in @ Xy @ B )
% 2.84/1.63 => ( ( kpair @ Xx @ Xy )
% 2.84/1.63 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodfstpairEq_type,type,
% 2.84/1.63 cartprodfstpairEq: $o ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodfstpairEq,definition,
% 2.84/1.63 ( cartprodfstpairEq
% 2.84/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.63 ( ( in @ Xx @ A )
% 2.84/1.63 => ! [Xy: $i] :
% 2.84/1.63 ( ( in @ Xy @ B )
% 2.84/1.63 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.84/1.63 = Xx ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodsndpairEq_type,type,
% 2.84/1.63 cartprodsndpairEq: $o ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodsndpairEq,definition,
% 2.84/1.63 ( cartprodsndpairEq
% 2.84/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.84/1.63 ( ( in @ Xx @ A )
% 2.84/1.63 => ! [Xy: $i] :
% 2.84/1.63 ( ( in @ Xy @ B )
% 2.84/1.63 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.84/1.63 = Xy ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodpairsurjEq_type,type,
% 2.84/1.63 cartprodpairsurjEq: $o ).
% 2.84/1.63
% 2.84/1.63 thf(cartprodpairsurjEq,definition,
% 2.84/1.63 ( cartprodpairsurjEq
% 2.84/1.63 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.84/1.63 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.84/1.63 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.84/1.63 = Xu ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(breln_type,type,
% 2.84/1.63 breln: $i > $i > $i > $o ).
% 2.84/1.63
% 2.84/1.63 thf(breln,definition,
% 2.84/1.63 ( breln
% 2.84/1.63 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstr_type,type,
% 2.84/1.63 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrI_type,type,
% 2.84/1.63 dpsetconstrI: $o ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrI,definition,
% 2.84/1.63 ( dpsetconstrI
% 2.84/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.84/1.63 ( ( in @ Xx @ A )
% 2.84/1.63 => ! [Xy: $i] :
% 2.84/1.63 ( ( in @ Xy @ B )
% 2.84/1.63 => ( ( Xphi @ Xx @ Xy )
% 2.84/1.63 => ( in @ ( kpair @ Xx @ Xy )
% 2.84/1.63 @ ( dpsetconstr @ A @ B
% 2.84/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrSub_type,type,
% 2.84/1.63 dpsetconstrSub: $o ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrSub,definition,
% 2.84/1.63 ( dpsetconstrSub
% 2.84/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.84/1.63 ( subset
% 2.84/1.63 @ ( dpsetconstr @ A @ B
% 2.84/1.63 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.84/1.63 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(setOfPairsIsBReln_type,type,
% 2.84/1.63 setOfPairsIsBReln: $o ).
% 2.84/1.63
% 2.84/1.63 thf(setOfPairsIsBReln,definition,
% 2.84/1.63 ( setOfPairsIsBReln
% 2.84/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.84/1.63 ( breln @ A @ B
% 2.84/1.63 @ ( dpsetconstr @ A @ B
% 2.84/1.63 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrERa_type,type,
% 2.84/1.63 dpsetconstrERa: $o ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrERa,definition,
% 2.84/1.63 ( dpsetconstrERa
% 2.84/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.84/1.63 ( ( in @ Xx @ A )
% 2.84/1.63 => ! [Xy: $i] :
% 2.84/1.63 ( ( in @ Xy @ B )
% 2.84/1.63 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.84/1.63 @ ( dpsetconstr @ A @ B
% 2.84/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.84/1.63 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrEL1_type,type,
% 2.84/1.63 dpsetconstrEL1: $o ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrEL1,definition,
% 2.84/1.63 ( dpsetconstrEL1
% 2.84/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.84/1.63 ( ( in @ ( kpair @ Xx @ Xy )
% 2.84/1.63 @ ( dpsetconstr @ A @ B
% 2.84/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.84/1.63 => ( in @ Xx @ A ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrEL2_type,type,
% 2.84/1.63 dpsetconstrEL2: $o ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrEL2,definition,
% 2.84/1.63 ( dpsetconstrEL2
% 2.84/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.84/1.63 ( ( in @ ( kpair @ Xx @ Xy )
% 2.84/1.63 @ ( dpsetconstr @ A @ B
% 2.84/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.84/1.63 => ( in @ Xy @ B ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrER_type,type,
% 2.84/1.63 dpsetconstrER: $o ).
% 2.84/1.63
% 2.84/1.63 thf(dpsetconstrER,definition,
% 2.84/1.63 ( dpsetconstrER
% 2.84/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.84/1.63 ( ( in @ ( kpair @ Xx @ Xy )
% 2.84/1.63 @ ( dpsetconstr @ A @ B
% 2.84/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.84/1.63 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(func_type,type,
% 2.84/1.63 func: $i > $i > $i > $o ).
% 2.84/1.63
% 2.84/1.63 thf(func,definition,
% 2.84/1.63 ( func
% 2.84/1.63 = ( ^ [A: $i,B: $i,R: $i] :
% 2.84/1.63 ( ( breln @ A @ B @ R )
% 2.84/1.63 & ! [Xx: $i] :
% 2.84/1.63 ( ( in @ Xx @ A )
% 2.84/1.63 => ( ex1 @ B
% 2.84/1.63 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(funcSet_type,type,
% 2.84/1.63 funcSet: $i > $i > $i ).
% 2.84/1.63
% 2.84/1.63 thf(funcSet,definition,
% 2.84/1.63 ( funcSet
% 2.84/1.63 = ( ^ [A: $i,B: $i] :
% 2.84/1.63 ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
% 2.84/1.63 @ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).
% 2.84/1.63
% 2.84/1.63 thf(funcImageSingleton,conjecture,
% 2.84/1.63 ( setextAx
% 2.84/1.63 => ( emptysetAx
% 2.84/1.63 => ( setadjoinAx
% 2.84/1.63 => ( powersetAx
% 2.84/1.63 => ( setunionAx
% 2.84/1.63 => ( omega0Ax
% 2.84/1.63 => ( omegaSAx
% 2.84/1.63 => ( omegaIndAx
% 2.84/1.63 => ( replAx
% 2.84/1.63 => ( foundationAx
% 2.84/1.63 => ( wellorderingAx
% 2.84/1.63 => ( descrp
% 2.84/1.63 => ( dsetconstrI
% 2.84/1.63 => ( dsetconstrEL
% 2.84/1.63 => ( dsetconstrER
% 2.84/1.63 => ( exuE1
% 2.84/1.63 => ( prop2setE
% 2.84/1.63 => ( emptysetE
% 2.84/1.63 => ( emptysetimpfalse
% 2.84/1.63 => ( notinemptyset
% 2.84/1.63 => ( exuE3e
% 2.84/1.63 => ( setext
% 2.84/1.63 => ( emptyI
% 2.84/1.63 => ( noeltsimpempty
% 2.84/1.63 => ( setbeta
% 2.84/1.63 => ( nonemptyE1
% 2.84/1.63 => ( nonemptyI
% 2.84/1.63 => ( nonemptyI1
% 2.84/1.63 => ( setadjoinIL
% 2.84/1.63 => ( emptyinunitempty
% 2.84/1.63 => ( setadjoinIR
% 2.84/1.63 => ( setadjoinE
% 2.84/1.63 => ( setadjoinOr
% 2.84/1.63 => ( setoftrueEq
% 2.84/1.63 => ( powersetI
% 2.84/1.63 => ( emptyinPowerset
% 2.84/1.63 => ( emptyInPowerset
% 2.84/1.63 => ( powersetE
% 2.84/1.63 => ( setunionI
% 2.84/1.63 => ( setunionE
% 2.84/1.63 => ( subPowSU
% 2.84/1.63 => ( exuE2
% 2.84/1.63 => ( nonemptyImpWitness
% 2.84/1.63 => ( uniqinunit
% 2.84/1.63 => ( notinsingleton
% 2.84/1.63 => ( eqinunit
% 2.84/1.63 => ( singletonsswitch
% 2.84/1.63 => ( upairsetE
% 2.84/1.63 => ( upairsetIL
% 2.84/1.63 => ( upairsetIR
% 2.84/1.63 => ( emptyE1
% 2.84/1.63 => ( vacuousDall
% 2.84/1.63 => ( quantDeMorgan1
% 2.84/1.63 => ( quantDeMorgan2
% 2.84/1.63 => ( quantDeMorgan3
% 2.84/1.63 => ( quantDeMorgan4
% 2.84/1.63 => ( prop2setI
% 2.84/1.63 => ( prop2set2propI
% 2.84/1.63 => ( notdexE
% 2.84/1.63 => ( notdallE
% 2.84/1.63 => ( exuI1
% 2.84/1.63 => ( exuI3
% 2.84/1.63 => ( exuI2
% 2.84/1.63 => ( inCongP
% 2.84/1.63 => ( in__Cong
% 2.84/1.63 => ( exuE3u
% 2.84/1.63 => ( exu__Cong
% 2.84/1.63 => ( emptyset__Cong
% 2.84/1.63 => ( setadjoin__Cong
% 2.84/1.63 => ( powerset__Cong
% 2.84/1.63 => ( setunion__Cong
% 2.84/1.63 => ( omega__Cong
% 2.84/1.63 => ( exuEu
% 2.84/1.63 => ( descr__Cong
% 2.84/1.63 => ( dsetconstr__Cong
% 2.84/1.63 => ( subsetI1
% 2.84/1.63 => ( eqimpsubset2
% 2.84/1.63 => ( eqimpsubset1
% 2.84/1.63 => ( subsetI2
% 2.84/1.63 => ( emptysetsubset
% 2.84/1.63 => ( subsetE
% 2.84/1.63 => ( subsetE2
% 2.84/1.63 => ( notsubsetI
% 2.84/1.63 => ( notequalI1
% 2.84/1.63 => ( notequalI2
% 2.84/1.63 => ( subsetRefl
% 2.84/1.63 => ( subsetTrans
% 2.84/1.63 => ( setadjoinSub
% 2.84/1.63 => ( setadjoinSub2
% 2.84/1.63 => ( subset2powerset
% 2.84/1.63 => ( setextsub
% 2.84/1.63 => ( subsetemptysetimpeq
% 2.84/1.63 => ( powersetI1
% 2.84/1.63 => ( powersetE1
% 2.84/1.63 => ( inPowerset
% 2.84/1.63 => ( powersetsubset
% 2.84/1.63 => ( sepInPowerset
% 2.84/1.63 => ( sepSubset
% 2.84/1.63 => ( binunionIL
% 2.84/1.63 => ( upairset2IR
% 2.84/1.63 => ( binunionIR
% 2.84/1.63 => ( binunionEcases
% 2.84/1.63 => ( binunionE
% 2.84/1.63 => ( binunionLsub
% 2.84/1.63 => ( binunionRsub
% 2.84/1.63 => ( binintersectI
% 2.84/1.63 => ( binintersectSubset5
% 2.84/1.63 => ( binintersectEL
% 2.84/1.63 => ( binintersectLsub
% 2.84/1.63 => ( binintersectSubset2
% 2.84/1.63 => ( binintersectSubset3
% 2.84/1.63 => ( binintersectER
% 2.84/1.63 => ( disjointsetsI1
% 2.84/1.63 => ( binintersectRsub
% 2.84/1.63 => ( binintersectSubset4
% 2.84/1.63 => ( binintersectSubset1
% 2.84/1.63 => ( bs114d
% 2.84/1.63 => ( setminusI
% 2.84/1.63 => ( setminusEL
% 2.84/1.63 => ( setminusER
% 2.84/1.63 => ( setminusSubset2
% 2.84/1.63 => ( setminusERneg
% 2.84/1.63 => ( setminusELneg
% 2.84/1.63 => ( setminusILneg
% 2.84/1.63 => ( setminusIRneg
% 2.84/1.63 => ( setminusLsub
% 2.84/1.63 => ( setminusSubset1
% 2.84/1.63 => ( symdiffE
% 2.84/1.63 => ( symdiffI1
% 2.84/1.63 => ( symdiffI2
% 2.84/1.63 => ( symdiffIneg1
% 2.84/1.63 => ( symdiffIneg2
% 2.84/1.63 => ( secondinupair
% 2.84/1.63 => ( setukpairIL
% 2.84/1.63 => ( setukpairIR
% 2.84/1.63 => ( kpairiskpair
% 2.84/1.63 => ( kpairp
% 2.84/1.63 => ( singletonsubset
% 2.84/1.63 => ( singletoninpowerset
% 2.84/1.63 => ( singletoninpowunion
% 2.84/1.63 => ( upairset2E
% 2.84/1.63 => ( upairsubunion
% 2.84/1.63 => ( upairinpowunion
% 2.84/1.63 => ( ubforcartprodlem1
% 2.84/1.63 => ( ubforcartprodlem2
% 2.84/1.63 => ( ubforcartprodlem3
% 2.84/1.63 => ( cartprodpairin
% 2.84/1.63 => ( cartprodmempair1
% 2.84/1.63 => ( cartprodmempair
% 2.84/1.63 => ( setunionE2
% 2.84/1.63 => ( setunionsingleton1
% 2.84/1.63 => ( setunionsingleton2
% 2.84/1.63 => ( setunionsingleton
% 2.84/1.63 => ( singletonprop
% 2.84/1.63 => ( ex1E1
% 2.84/1.63 => ( ex1I
% 2.84/1.63 => ( ex1I2
% 2.84/1.63 => ( singletonsuniq
% 2.84/1.63 => ( setukpairinjL1
% 2.84/1.63 => ( kfstsingleton
% 2.84/1.63 => ( theprop
% 2.84/1.63 => ( kfstpairEq
% 2.84/1.63 => ( cartprodfstin
% 2.84/1.63 => ( setukpairinjL2
% 2.84/1.63 => ( setukpairinjL
% 2.84/1.63 => ( setukpairinjR11
% 2.84/1.63 => ( setukpairinjR12
% 2.84/1.63 => ( setukpairinjR1
% 2.84/1.63 => ( upairequniteq
% 2.84/1.63 => ( setukpairinjR2
% 2.84/1.63 => ( setukpairinjR
% 2.84/1.63 => ( ksndsingleton
% 2.84/1.63 => ( ksndpairEq
% 2.84/1.63 => ( kpairsurjEq
% 2.84/1.63 => ( cartprodsndin
% 2.84/1.63 => ( cartprodpairmemEL
% 2.84/1.63 => ( cartprodpairmemER
% 2.84/1.63 => ( cartprodmempaircEq
% 2.84/1.63 => ( cartprodfstpairEq
% 2.84/1.63 => ( cartprodsndpairEq
% 2.84/1.63 => ( cartprodpairsurjEq
% 2.84/1.63 => ( dpsetconstrI
% 2.84/1.63 => ( dpsetconstrSub
% 2.84/1.63 => ( setOfPairsIsBReln
% 2.84/1.63 => ( dpsetconstrERa
% 2.84/1.63 => ( dpsetconstrEL1
% 2.84/1.63 => ( dpsetconstrEL2
% 2.84/1.63 => ( dpsetconstrER
% 2.84/1.63 => ! [A: $i,B: $i,Xf: $i] :
% 2.84/1.63 ( ( func @ A @ B @ Xf )
% 2.84/1.63 => ! [Xx: $i] :
% 2.84/1.63 ( ( in @ Xx @ A )
% 2.84/1.63 => ( singleton
% 2.84/1.63 @ ( dsetconstr @ B
% 2.84/1.63 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.63 ------------------------
% 2.84/1.66 % (17269)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/4Mi)
% 2.84/1.66 % (17268)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/183Mi)
% 2.84/1.66 % (17270)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/27Mi)
% 2.84/1.66 % (17271)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/2Mi)
% 2.84/1.66 % (17274)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/18Mi)
% 2.84/1.66 % (17273)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/275Mi)
% 2.84/1.66 % (17272)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/2Mi)
% 2.84/1.66 % (17269)Instruction limit reached!
% 2.84/1.66 % (17269)------------------------------
% 2.84/1.66 % (17269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.66 % (17269)Termination reason: Unknown
% 2.84/1.66 % (17269)Termination phase: shuffling
% 2.84/1.66
% 2.84/1.66 % (17269)Memory used [KB]: 1407
% 2.84/1.66 % (17269)Time elapsed: 0.004 s
% 2.84/1.66 % (17269)Instructions burned: 5 (million)
% 2.84/1.66 % (17269)------------------------------
% 2.84/1.66 % (17269)------------------------------
% 2.84/1.66 % (17271)Instruction limit reached!
% 2.84/1.66 % (17271)------------------------------
% 2.84/1.66 % (17271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.66 % (17271)Termination reason: Unknown
% 2.84/1.66 % (17271)Termination phase: shuffling
% 2.84/1.66
% 2.84/1.66 % (17272)Instruction limit reached!
% 2.84/1.66 % (17272)------------------------------
% 2.84/1.66 % (17272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.66 % (17272)Termination reason: Unknown
% 2.84/1.66 % (17272)Termination phase: shuffling
% 2.84/1.66
% 2.84/1.66 % (17272)Memory used [KB]: 1407
% 2.84/1.66 % (17272)Time elapsed: 0.003 s
% 2.84/1.66 % (17272)Instructions burned: 2 (million)
% 2.84/1.66 % (17272)------------------------------
% 2.84/1.66 % (17272)------------------------------
% 2.84/1.66 % (17271)Memory used [KB]: 1407
% 2.84/1.66 % (17271)Time elapsed: 0.003 s
% 2.84/1.66 % (17271)Instructions burned: 2 (million)
% 2.84/1.66 % (17271)------------------------------
% 2.84/1.66 % (17271)------------------------------
% 2.84/1.67 % (17274)Instruction limit reached!
% 2.84/1.67 % (17274)------------------------------
% 2.84/1.67 % (17274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.67 % (17274)Termination reason: Unknown
% 2.84/1.67 % (17274)Termination phase: Property scanning
% 2.84/1.67
% 2.84/1.67 % (17274)Memory used [KB]: 1663
% 2.84/1.67 % (17274)Time elapsed: 0.011 s
% 2.84/1.67 % (17274)Instructions burned: 19 (million)
% 2.84/1.67 % (17274)------------------------------
% 2.84/1.67 % (17274)------------------------------
% 2.84/1.67 % (17270)Instruction limit reached!
% 2.84/1.67 % (17270)------------------------------
% 2.84/1.67 % (17270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.67 % (17270)Termination reason: Unknown
% 2.84/1.67 % (17270)Termination phase: shuffling
% 2.84/1.67
% 2.84/1.67 % (17270)Memory used [KB]: 1918
% 2.84/1.67 % (17270)Time elapsed: 0.015 s
% 2.84/1.67 % (17270)Instructions burned: 28 (million)
% 2.84/1.67 % (17270)------------------------------
% 2.84/1.67 % (17270)------------------------------
% 2.84/1.67 % (17275)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/3Mi)
% 2.84/1.67 % (17277)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/15Mi)
% 2.84/1.67 % (17276)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/37Mi)
% 2.84/1.68 % (17275)Instruction limit reached!
% 2.84/1.68 % (17275)------------------------------
% 2.84/1.68 % (17275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.68 % (17275)Termination reason: Unknown
% 2.84/1.68 % (17275)Termination phase: shuffling
% 2.84/1.68
% 2.84/1.68 % (17275)Memory used [KB]: 1407
% 2.84/1.68 % (17275)Time elapsed: 0.003 s
% 2.84/1.68 % (17275)Instructions burned: 4 (million)
% 2.84/1.68 % (17275)------------------------------
% 2.84/1.68 % (17275)------------------------------
% 2.84/1.68 % (17277)Instruction limit reached!
% 2.84/1.68 % (17277)------------------------------
% 2.84/1.68 % (17277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.68 % (17277)Termination reason: Unknown
% 2.84/1.68 % (17277)Termination phase: shuffling
% 2.84/1.68
% 2.84/1.68 % (17277)Memory used [KB]: 1663
% 2.84/1.68 % (17277)Time elapsed: 0.009 s
% 2.84/1.68 % (17277)Instructions burned: 16 (million)
% 2.84/1.68 % (17277)------------------------------
% 2.84/1.68 % (17277)------------------------------
% 2.84/1.68 % (17278)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/3Mi)
% 2.84/1.69 % (17278)Instruction limit reached!
% 2.84/1.69 % (17278)------------------------------
% 2.84/1.69 % (17278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.69 % (17278)Termination reason: Unknown
% 2.84/1.69 % (17278)Termination phase: shuffling
% 2.84/1.69
% 2.84/1.69 % (17278)Memory used [KB]: 1407
% 2.84/1.69 % (17278)Time elapsed: 0.004 s
% 2.84/1.69 % (17278)Instructions burned: 4 (million)
% 2.84/1.69 % (17278)------------------------------
% 2.84/1.69 % (17278)------------------------------
% 2.84/1.69 % (17279)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/1041Mi)
% 2.84/1.69 % (17280)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/7Mi)
% 2.84/1.69 % (17276)Instruction limit reached!
% 2.84/1.69 % (17276)------------------------------
% 2.84/1.69 % (17276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.69 % (17276)Termination reason: Unknown
% 2.84/1.69 % (17276)Termination phase: Property scanning
% 2.84/1.69
% 2.84/1.69 % (17276)Memory used [KB]: 1918
% 2.84/1.69 % (17276)Time elapsed: 0.018 s
% 2.84/1.69 % (17276)Instructions burned: 37 (million)
% 2.84/1.69 % (17276)------------------------------
% 2.84/1.69 % (17276)------------------------------
% 2.84/1.69 % (17280)Instruction limit reached!
% 2.84/1.69 % (17280)------------------------------
% 2.84/1.69 % (17280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.69 % (17280)Termination reason: Unknown
% 2.84/1.69 % (17280)Termination phase: shuffling
% 2.84/1.69
% 2.84/1.69 % (17280)Memory used [KB]: 1535
% 2.84/1.69 % (17280)Time elapsed: 0.005 s
% 2.84/1.69 % (17280)Instructions burned: 9 (million)
% 2.84/1.69 % (17280)------------------------------
% 2.84/1.69 % (17280)------------------------------
% 2.88/1.70 % (17281)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/16Mi)
% 2.88/1.70 % (17282)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/3Mi)
% 2.88/1.70 % (17282)Instruction limit reached!
% 2.88/1.70 % (17282)------------------------------
% 2.88/1.70 % (17282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.70 % (17282)Termination reason: Unknown
% 2.88/1.70 % (17282)Termination phase: shuffling
% 2.88/1.70
% 2.88/1.70 % (17282)Memory used [KB]: 1407
% 2.88/1.70 % (17282)Time elapsed: 0.004 s
% 2.88/1.70 % (17282)Instructions burned: 4 (million)
% 2.88/1.70 % (17282)------------------------------
% 2.88/1.70 % (17282)------------------------------
% 2.88/1.71 % (17281)Instruction limit reached!
% 2.88/1.71 % (17281)------------------------------
% 2.88/1.71 % (17281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.71 % (17281)Termination reason: Unknown
% 2.88/1.71 % (17281)Termination phase: shuffling
% 2.88/1.71
% 2.88/1.71 % (17281)Memory used [KB]: 1663
% 2.88/1.71 % (17281)Time elapsed: 0.010 s
% 2.88/1.71 % (17281)Instructions burned: 17 (million)
% 2.88/1.71 % (17281)------------------------------
% 2.88/1.71 % (17281)------------------------------
% 2.88/1.71 % (17283)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/3Mi)
% 2.88/1.71 % (17283)Instruction limit reached!
% 2.88/1.71 % (17283)------------------------------
% 2.88/1.71 % (17283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.71 % (17283)Termination reason: Unknown
% 2.88/1.71 % (17283)Termination phase: shuffling
% 2.88/1.71
% 2.88/1.71 % (17283)Memory used [KB]: 1407
% 2.88/1.71 % (17283)Time elapsed: 0.003 s
% 2.88/1.71 % (17283)Instructions burned: 4 (million)
% 2.88/1.71 % (17283)------------------------------
% 2.88/1.71 % (17283)------------------------------
% 2.88/1.71 % (17284)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/7Mi)
% 2.88/1.71 % (17284)Instruction limit reached!
% 2.88/1.71 % (17284)------------------------------
% 2.88/1.71 % (17284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.71 % (17284)Termination reason: Unknown
% 2.88/1.71 % (17284)Termination phase: shuffling
% 2.88/1.71
% 2.88/1.71 % (17284)Memory used [KB]: 1407
% 2.88/1.71 % (17284)Time elapsed: 0.005 s
% 2.88/1.71 % (17284)Instructions burned: 7 (million)
% 2.88/1.71 % (17284)------------------------------
% 2.88/1.71 % (17284)------------------------------
% 2.88/1.72 % (17285)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/3Mi)
% 2.88/1.72 % (17285)Instruction limit reached!
% 2.88/1.72 % (17285)------------------------------
% 2.88/1.72 % (17285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.72 % (17285)Termination reason: Unknown
% 2.88/1.72 % (17285)Termination phase: shuffling
% 2.88/1.72
% 2.88/1.72 % (17285)Memory used [KB]: 1407
% 2.88/1.72 % (17285)Time elapsed: 0.003 s
% 2.88/1.72 % (17285)Instructions burned: 3 (million)
% 2.88/1.72 % (17285)------------------------------
% 2.88/1.72 % (17285)------------------------------
% 2.88/1.72 % (17286)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/4Mi)
% 2.88/1.72 % (17287)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/18Mi)
% 2.88/1.72 % (17286)Instruction limit reached!
% 2.88/1.72 % (17286)------------------------------
% 2.88/1.72 % (17286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.72 % (17286)Termination reason: Unknown
% 2.88/1.72 % (17286)Termination phase: shuffling
% 2.88/1.72
% 2.88/1.72 % (17286)Memory used [KB]: 1407
% 2.88/1.72 % (17286)Time elapsed: 0.004 s
% 2.88/1.72 % (17286)Instructions burned: 5 (million)
% 2.88/1.72 % (17286)------------------------------
% 2.88/1.72 % (17286)------------------------------
% 2.88/1.73 % (17288)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/710Mi)
% 2.88/1.73 % (17287)Instruction limit reached!
% 2.88/1.73 % (17287)------------------------------
% 2.88/1.73 % (17287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.73 % (17287)Termination reason: Unknown
% 2.88/1.73 % (17287)Termination phase: shuffling
% 2.88/1.73
% 2.88/1.73 % (17287)Memory used [KB]: 1791
% 2.88/1.73 % (17287)Time elapsed: 0.010 s
% 2.88/1.73 % (17287)Instructions burned: 19 (million)
% 2.88/1.73 % (17287)------------------------------
% 2.88/1.73 % (17287)------------------------------
% 2.88/1.74 % (17268)Instruction limit reached!
% 2.88/1.74 % (17268)------------------------------
% 2.88/1.74 % (17268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.74 % (17268)Termination reason: Unknown
% 2.88/1.74 % (17268)Termination phase: Saturation
% 2.88/1.74
% 2.88/1.74 % (17268)Memory used [KB]: 7547
% 2.88/1.74 % (17268)Time elapsed: 0.082 s
% 2.88/1.74 % (17268)Instructions burned: 184 (million)
% 2.88/1.74 % (17268)------------------------------
% 2.88/1.74 % (17268)------------------------------
% 2.88/1.74 % (17289)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/6Mi)
% 2.88/1.74 % (17289)Instruction limit reached!
% 2.88/1.74 % (17289)------------------------------
% 2.88/1.74 % (17289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.74 % (17289)Termination reason: Unknown
% 2.88/1.74 % (17289)Termination phase: shuffling
% 2.88/1.74
% 2.88/1.74 % (17289)Memory used [KB]: 1535
% 2.88/1.74 % (17289)Time elapsed: 0.005 s
% 2.88/1.74 % (17289)Instructions burned: 7 (million)
% 2.88/1.74 % (17289)------------------------------
% 2.88/1.74 % (17289)------------------------------
% 2.88/1.74 % (17290)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/902Mi)
% 2.88/1.75 % (17291)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/21Mi)
% 2.88/1.75 % (17292)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17169 for (2999ds/5Mi)
% 2.88/1.76 % (17292)Instruction limit reached!
% 2.88/1.76 % (17292)------------------------------
% 2.88/1.76 % (17292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.76 % (17292)Termination reason: Unknown
% 2.88/1.76 % (17292)Termination phase: shuffling
% 2.88/1.76
% 2.88/1.76 % (17292)Memory used [KB]: 1407
% 2.88/1.76 % (17292)Time elapsed: 0.004 s
% 2.88/1.76 % (17292)Instructions burned: 5 (million)
% 2.88/1.76 % (17292)------------------------------
% 2.88/1.76 % (17292)------------------------------
% 2.88/1.76 % (17293)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_17169 for (2998ds/6Mi)
% 2.88/1.76 % (17291)Instruction limit reached!
% 2.88/1.76 % (17291)------------------------------
% 2.88/1.76 % (17291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.76 % (17291)Termination reason: Unknown
% 2.88/1.76 % (17291)Termination phase: shuffling
% 2.88/1.76
% 2.88/1.76 % (17291)Memory used [KB]: 1791
% 2.88/1.76 % (17291)Time elapsed: 0.012 s
% 2.88/1.76 % (17291)Instructions burned: 22 (million)
% 2.88/1.76 % (17291)------------------------------
% 2.88/1.76 % (17291)------------------------------
% 2.88/1.76 % (17293)Instruction limit reached!
% 2.88/1.76 % (17293)------------------------------
% 2.88/1.76 % (17293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.76 % (17293)Termination reason: Unknown
% 2.88/1.76 % (17293)Termination phase: shuffling
% 2.88/1.76
% 2.88/1.76 % (17293)Memory used [KB]: 1407
% 2.88/1.76 % (17293)Time elapsed: 0.005 s
% 2.88/1.76 % (17293)Instructions burned: 7 (million)
% 2.88/1.76 % (17293)------------------------------
% 2.88/1.76 % (17293)------------------------------
% 2.88/1.77 % (17294)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17169 for (2998ds/377Mi)
% 2.88/1.77 % (17295)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_17169 for (2998ds/779Mi)
% 2.88/1.77 % (17296)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_17169 for (2998ds/19Mi)
% 2.88/1.78 % (17296)Instruction limit reached!
% 2.88/1.78 % (17296)------------------------------
% 2.88/1.78 % (17296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.78 % (17296)Termination reason: Unknown
% 2.88/1.78 % (17296)Termination phase: shuffling
% 2.88/1.78
% 2.88/1.78 % (17296)Memory used [KB]: 1791
% 2.88/1.78 % (17296)Time elapsed: 0.010 s
% 2.88/1.78 % (17296)Instructions burned: 19 (million)
% 2.88/1.78 % (17296)------------------------------
% 2.88/1.78 % (17296)------------------------------
% 2.88/1.79 % (17273)Instruction limit reached!
% 2.88/1.79 % (17273)------------------------------
% 2.88/1.79 % (17273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.79 % (17273)Termination reason: Unknown
% 2.88/1.79 % (17273)Termination phase: Saturation
% 2.88/1.79
% 2.88/1.79 % (17273)Memory used [KB]: 8443
% 2.88/1.79 % (17273)Time elapsed: 0.136 s
% 2.88/1.79 % (17273)Instructions burned: 275 (million)
% 2.88/1.79 % (17273)------------------------------
% 2.88/1.79 % (17273)------------------------------
% 2.88/1.80 % (17297)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_17169 for (2998ds/879Mi)
% 2.88/1.81 % (17298)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17169 for (2998ds/17Mi)
% 2.88/1.82 % (17298)Instruction limit reached!
% 2.88/1.82 % (17298)------------------------------
% 2.88/1.82 % (17298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.82 % (17298)Termination reason: Unknown
% 2.88/1.82 % (17298)Termination phase: shuffling
% 2.88/1.82
% 2.88/1.82 % (17298)Memory used [KB]: 1791
% 2.88/1.82 % (17298)Time elapsed: 0.010 s
% 2.88/1.82 % (17298)Instructions burned: 18 (million)
% 2.88/1.82 % (17298)------------------------------
% 2.88/1.82 % (17298)------------------------------
% 2.88/1.83 % (17299)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17169 for (2998ds/3Mi)
% 2.88/1.84 % (17299)Instruction limit reached!
% 2.88/1.84 % (17299)------------------------------
% 2.88/1.84 % (17299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.84 % (17299)Termination reason: Unknown
% 2.88/1.84 % (17299)Termination phase: shuffling
% 2.88/1.84
% 2.88/1.84 % (17299)Memory used [KB]: 1407
% 2.88/1.84 % (17299)Time elapsed: 0.004 s
% 2.88/1.84 % (17299)Instructions burned: 3 (million)
% 2.88/1.84 % (17299)------------------------------
% 2.88/1.84 % (17299)------------------------------
% 2.88/1.85 % (17300)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_17169 for (2998ds/30Mi)
% 2.88/1.87 % (17300)Instruction limit reached!
% 2.88/1.87 % (17300)------------------------------
% 2.88/1.87 % (17300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.87 % (17300)Termination reason: Unknown
% 2.88/1.87 % (17300)Termination phase: shuffling
% 2.88/1.87
% 2.88/1.87 % (17300)Memory used [KB]: 1918
% 2.88/1.87 % (17300)Time elapsed: 0.016 s
% 2.88/1.87 % (17300)Instructions burned: 30 (million)
% 2.88/1.87 % (17300)------------------------------
% 2.88/1.87 % (17300)------------------------------
% 2.88/1.88 % (17301)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_17169 for (2997ds/127Mi)
% 2.88/1.94 % (17301)Instruction limit reached!
% 2.88/1.94 % (17301)------------------------------
% 2.88/1.94 % (17301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.94 % (17301)Termination reason: Unknown
% 2.88/1.94 % (17301)Termination phase: Saturation
% 2.88/1.94
% 2.88/1.94 % (17301)Memory used [KB]: 6908
% 2.88/1.94 % (17301)Time elapsed: 0.058 s
% 2.88/1.94 % (17301)Instructions burned: 127 (million)
% 2.88/1.94 % (17301)------------------------------
% 2.88/1.94 % (17301)------------------------------
% 2.88/1.95 % (17294)Instruction limit reached!
% 2.88/1.95 % (17294)------------------------------
% 2.88/1.95 % (17294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.95 % (17294)Termination reason: Unknown
% 2.88/1.95 % (17294)Termination phase: Saturation
% 2.88/1.95
% 2.88/1.95 % (17294)Memory used [KB]: 8315
% 2.88/1.95 % (17294)Time elapsed: 0.180 s
% 2.88/1.95 % (17294)Instructions burned: 377 (million)
% 2.88/1.95 % (17294)------------------------------
% 2.88/1.95 % (17294)------------------------------
% 2.88/1.96 % (17302)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_17169 for (2997ds/100Mi)
% 2.88/1.97 % (17303)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_17169 for (2996ds/3Mi)
% 2.88/1.97 % (17303)Instruction limit reached!
% 2.88/1.97 % (17303)------------------------------
% 2.88/1.97 % (17303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.97 % (17303)Termination reason: Unknown
% 2.88/1.97 % (17303)Termination phase: shuffling
% 2.88/1.97
% 2.88/1.97 % (17303)Memory used [KB]: 1407
% 2.88/1.97 % (17303)Time elapsed: 0.003 s
% 2.88/1.97 % (17303)Instructions burned: 3 (million)
% 2.88/1.97 % (17303)------------------------------
% 2.88/1.97 % (17303)------------------------------
% 2.88/1.99 % (17304)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_17169 for (2996ds/20Mi)
% 2.88/2.00 % (17304)Instruction limit reached!
% 2.88/2.00 % (17304)------------------------------
% 2.88/2.00 % (17304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/2.00 % (17304)Termination reason: Unknown
% 2.88/2.00 % (17304)Termination phase: Property scanning
% 2.88/2.00
% 2.88/2.00 % (17304)Memory used [KB]: 1791
% 2.88/2.00 % (17304)Time elapsed: 0.013 s
% 2.88/2.00 % (17304)Instructions burned: 21 (million)
% 2.88/2.00 % (17304)------------------------------
% 2.88/2.00 % (17304)------------------------------
% 2.88/2.00 % (17302)Instruction limit reached!
% 2.88/2.00 % (17302)------------------------------
% 2.88/2.00 % (17302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/2.00 % (17302)Termination reason: Unknown
% 2.88/2.00 % (17302)Termination phase: Saturation
% 2.88/2.00
% 2.88/2.00 % (17302)Memory used [KB]: 6780
% 2.88/2.00 % (17302)Time elapsed: 0.046 s
% 2.88/2.00 % (17302)Instructions burned: 100 (million)
% 2.88/2.00 % (17302)------------------------------
% 2.88/2.00 % (17302)------------------------------
% 2.88/2.01 % (17305)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_17169 for (2996ds/86Mi)
% 2.88/2.02 % (17306)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_17169 for (2996ds/107Mi)
% 5.46/2.05 % (17305)Instruction limit reached!
% 5.46/2.05 % (17305)------------------------------
% 5.46/2.05 % (17305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.05 % (17305)Termination reason: Unknown
% 5.46/2.05 % (17305)Termination phase: Property scanning
% 5.46/2.05
% 5.46/2.05 % (17305)Memory used [KB]: 2174
% 5.46/2.05 % (17305)Time elapsed: 0.038 s
% 5.46/2.05 % (17305)Instructions burned: 86 (million)
% 5.46/2.05 % (17305)------------------------------
% 5.46/2.05 % (17305)------------------------------
% 5.46/2.06 % (17295)Instruction limit reached!
% 5.46/2.06 % (17295)------------------------------
% 5.46/2.06 % (17295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.06 % (17295)Termination reason: Unknown
% 5.46/2.06 % (17295)Termination phase: Saturation
% 5.46/2.06
% 5.46/2.06 % (17295)Memory used [KB]: 7036
% 5.46/2.06 % (17295)Time elapsed: 0.292 s
% 5.46/2.06 % (17295)Instructions burned: 780 (million)
% 5.46/2.06 % (17295)------------------------------
% 5.46/2.06 % (17295)------------------------------
% 5.46/2.07 % (17307)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_17169 for (2995ds/39Mi)
% 5.46/2.07 % (17306)Instruction limit reached!
% 5.46/2.07 % (17306)------------------------------
% 5.46/2.07 % (17306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.07 % (17306)Termination reason: Unknown
% 5.46/2.07 % (17306)Termination phase: Saturation
% 5.46/2.07
% 5.46/2.07 % (17306)Memory used [KB]: 6652
% 5.46/2.07 % (17306)Time elapsed: 0.049 s
% 5.46/2.07 % (17306)Instructions burned: 107 (million)
% 5.46/2.07 % (17306)------------------------------
% 5.46/2.07 % (17306)------------------------------
% 5.46/2.07 % (17288)Instruction limit reached!
% 5.46/2.07 % (17288)------------------------------
% 5.46/2.07 % (17288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.07 % (17288)Termination reason: Unknown
% 5.46/2.07 % (17288)Termination phase: Saturation
% 5.46/2.07
% 5.46/2.07 % (17288)Memory used [KB]: 9466
% 5.46/2.07 % (17288)Time elapsed: 0.344 s
% 5.46/2.07 % (17288)Instructions burned: 710 (million)
% 5.46/2.07 % (17288)------------------------------
% 5.46/2.07 % (17288)------------------------------
% 5.46/2.08 % (17308)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_17169 for (2995ds/448Mi)
% 5.46/2.08 % (17279)Instruction limit reached!
% 5.46/2.08 % (17279)------------------------------
% 5.46/2.08 % (17279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.08 % (17279)Termination reason: Unknown
% 5.46/2.08 % (17279)Termination phase: Saturation
% 5.46/2.08
% 5.46/2.08 % (17279)Memory used [KB]: 11129
% 5.46/2.08 % (17279)Time elapsed: 0.397 s
% 5.46/2.08 % (17279)Instructions burned: 1043 (million)
% 5.46/2.08 % (17279)------------------------------
% 5.46/2.08 % (17279)------------------------------
% 5.46/2.08 % (17309)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_17169 for (2995ds/46Mi)
% 5.46/2.08 % (17310)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_17169 for (2995ds/98Mi)
% 5.46/2.08 % (17307)Instruction limit reached!
% 5.46/2.08 % (17307)------------------------------
% 5.46/2.08 % (17307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.08 % (17307)Termination reason: Unknown
% 5.46/2.08 % (17307)Termination phase: Property scanning
% 5.46/2.08
% 5.46/2.08 % (17307)Memory used [KB]: 1918
% 5.46/2.08 % (17307)Time elapsed: 0.020 s
% 5.46/2.08 % (17307)Instructions burned: 40 (million)
% 5.46/2.08 % (17307)------------------------------
% 5.46/2.08 % (17307)------------------------------
% 5.46/2.10 % (17311)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_17169 for (2995ds/507Mi)
% 5.46/2.10 % (17312)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_17169 for (2995ds/149Mi)
% 5.46/2.11 % (17309)Instruction limit reached!
% 5.46/2.11 % (17309)------------------------------
% 5.46/2.11 % (17309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.11 % (17309)Termination reason: Unknown
% 5.46/2.11 % (17309)Termination phase: Property scanning
% 5.46/2.11
% 5.46/2.11 % (17309)Memory used [KB]: 1918
% 5.46/2.11 % (17309)Time elapsed: 0.024 s
% 5.46/2.11 % (17309)Instructions burned: 47 (million)
% 5.46/2.11 % (17309)------------------------------
% 5.46/2.11 % (17309)------------------------------
% 6.02/2.12 % (17313)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_17169 for (2995ds/39Mi)
% 6.02/2.13 % (17310)Instruction limit reached!
% 6.02/2.13 % (17310)------------------------------
% 6.02/2.13 % (17310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.13 % (17310)Termination reason: Unknown
% 6.02/2.13 % (17310)Termination phase: Saturation
% 6.02/2.13
% 6.02/2.13 % (17310)Memory used [KB]: 2174
% 6.02/2.13 % (17310)Time elapsed: 0.045 s
% 6.02/2.13 % (17310)Instructions burned: 99 (million)
% 6.02/2.13 % (17310)------------------------------
% 6.02/2.13 % (17310)------------------------------
% 6.02/2.14 % (17313)Instruction limit reached!
% 6.02/2.14 % (17313)------------------------------
% 6.02/2.14 % (17313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.14 % (17313)Termination reason: Unknown
% 6.02/2.14 % (17313)Termination phase: Property scanning
% 6.02/2.14
% 6.02/2.14 % (17313)Memory used [KB]: 1918
% 6.02/2.14 % (17313)Time elapsed: 0.020 s
% 6.02/2.14 % (17313)Instructions burned: 40 (million)
% 6.02/2.14 % (17313)------------------------------
% 6.02/2.14 % (17313)------------------------------
% 6.02/2.14 % (17314)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_17169 for (2995ds/6Mi)
% 6.02/2.15 % (17314)Instruction limit reached!
% 6.02/2.15 % (17314)------------------------------
% 6.02/2.15 % (17314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.15 % (17314)Termination reason: Unknown
% 6.02/2.15 % (17314)Termination phase: shuffling
% 6.02/2.15
% 6.02/2.15 % (17314)Memory used [KB]: 1407
% 6.02/2.15 % (17314)Time elapsed: 0.005 s
% 6.02/2.15 % (17314)Instructions burned: 7 (million)
% 6.02/2.15 % (17314)------------------------------
% 6.02/2.15 % (17314)------------------------------
% 6.02/2.16 % (17315)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_17169 for (2994ds/1087Mi)
% 6.02/2.16 % (17316)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_17169 for (2994ds/47Mi)
% 6.02/2.17 % (17312)Instruction limit reached!
% 6.02/2.17 % (17312)------------------------------
% 6.02/2.17 % (17312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.17 % (17312)Termination reason: Unknown
% 6.02/2.17 % (17312)Termination phase: Saturation
% 6.02/2.17
% 6.02/2.17 % (17312)Memory used [KB]: 7419
% 6.02/2.17 % (17312)Time elapsed: 0.068 s
% 6.02/2.17 % (17312)Instructions burned: 150 (million)
% 6.02/2.17 % (17312)------------------------------
% 6.02/2.17 % (17312)------------------------------
% 6.02/2.18 % (17317)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_17169 for (2994ds/44Mi)
% 6.02/2.18 % (17316)Instruction limit reached!
% 6.02/2.18 % (17316)------------------------------
% 6.02/2.18 % (17316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.18 % (17316)Termination reason: Unknown
% 6.02/2.18 % (17316)Termination phase: Preprocessing 1
% 6.02/2.18
% 6.02/2.18 % (17316)Memory used [KB]: 1918
% 6.02/2.18 % (17316)Time elapsed: 0.022 s
% 6.02/2.18 % (17316)Instructions burned: 49 (million)
% 6.02/2.18 % (17316)------------------------------
% 6.02/2.18 % (17316)------------------------------
% 6.02/2.18 % (17290)Instruction limit reached!
% 6.02/2.18 % (17290)------------------------------
% 6.02/2.18 % (17290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.18 % (17290)Termination reason: Unknown
% 6.02/2.18 % (17290)Termination phase: Saturation
% 6.02/2.18
% 6.02/2.18 % (17290)Memory used [KB]: 9850
% 6.02/2.18 % (17290)Time elapsed: 0.444 s
% 6.02/2.18 % (17290)Instructions burned: 902 (million)
% 6.02/2.18 % (17290)------------------------------
% 6.02/2.18 % (17290)------------------------------
% 6.40/2.20 % (17318)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_17169 for (2994ds/432Mi)
% 6.40/2.20 % (17319)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_17169 for (2994ds/62Mi)
% 6.40/2.20 % (17317)Instruction limit reached!
% 6.40/2.20 % (17317)------------------------------
% 6.40/2.20 % (17317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.20 % (17317)Termination reason: Unknown
% 6.40/2.20 % (17317)Termination phase: Property scanning
% 6.40/2.20
% 6.40/2.20 % (17317)Memory used [KB]: 1918
% 6.40/2.20 % (17317)Time elapsed: 0.021 s
% 6.40/2.20 % (17317)Instructions burned: 45 (million)
% 6.40/2.20 % (17317)------------------------------
% 6.40/2.20 % (17317)------------------------------
% 6.40/2.22 % (17320)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17169 for (2994ds/31Mi)
% 6.40/2.23 % (17319)Instruction limit reached!
% 6.40/2.23 % (17319)------------------------------
% 6.40/2.23 % (17319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.23 % (17319)Termination reason: Unknown
% 6.40/2.23 % (17319)Termination phase: Property scanning
% 6.40/2.23
% 6.40/2.23 % (17319)Memory used [KB]: 2046
% 6.40/2.23 % (17319)Time elapsed: 0.030 s
% 6.40/2.23 % (17319)Instructions burned: 64 (million)
% 6.40/2.23 % (17319)------------------------------
% 6.40/2.23 % (17319)------------------------------
% 6.40/2.23 % (17320)Instruction limit reached!
% 6.40/2.23 % (17320)------------------------------
% 6.40/2.23 % (17320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.23 % (17320)Termination reason: Unknown
% 6.40/2.23 % (17320)Termination phase: Property scanning
% 6.40/2.23
% 6.40/2.23 % (17320)Memory used [KB]: 1918
% 6.40/2.23 % (17320)Time elapsed: 0.016 s
% 6.40/2.23 % (17320)Instructions burned: 32 (million)
% 6.40/2.23 % (17320)------------------------------
% 6.40/2.23 % (17320)------------------------------
% 6.40/2.23 % (17297)Instruction limit reached!
% 6.40/2.23 % (17297)------------------------------
% 6.40/2.23 % (17297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.23 % (17297)Termination reason: Unknown
% 6.40/2.23 % (17297)Termination phase: Saturation
% 6.40/2.23
% 6.40/2.23 % (17297)Memory used [KB]: 8443
% 6.40/2.23 % (17297)Time elapsed: 0.436 s
% 6.40/2.23 % (17297)Instructions burned: 880 (million)
% 6.40/2.23 % (17297)------------------------------
% 6.40/2.23 % (17297)------------------------------
% 6.40/2.25 % (17322)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_17169 for (2994ds/453Mi)
% 6.40/2.25 % (17321)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_17169 for (2994ds/96Mi)
% 6.40/2.25 % (17308)Instruction limit reached!
% 6.40/2.25 % (17308)------------------------------
% 6.40/2.25 % (17308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.25 % (17308)Termination reason: Unknown
% 6.40/2.25 % (17308)Termination phase: Saturation
% 6.40/2.25
% 6.40/2.25 % (17308)Memory used [KB]: 6908
% 6.40/2.25 % (17308)Time elapsed: 0.173 s
% 6.40/2.25 % (17308)Instructions burned: 448 (million)
% 6.40/2.25 % (17308)------------------------------
% 6.40/2.25 % (17308)------------------------------
% 6.40/2.25 % (17323)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_17169 for (2994ds/71Mi)
% 6.40/2.27 % (17324)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_17169 for (2993ds/83Mi)
% 6.40/2.28 % (17323)Instruction limit reached!
% 6.40/2.28 % (17323)------------------------------
% 6.40/2.28 % (17323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.28 % (17323)Termination reason: Unknown
% 6.40/2.28 % (17323)Termination phase: Function definition elimination
% 6.40/2.28
% 6.40/2.28 % (17323)Memory used [KB]: 2174
% 6.40/2.28 % (17323)Time elapsed: 0.034 s
% 6.40/2.28 % (17323)Instructions burned: 73 (million)
% 6.40/2.28 % (17323)------------------------------
% 6.40/2.28 % (17323)------------------------------
% 6.40/2.29 % (17321)Instruction limit reached!
% 6.40/2.29 % (17321)------------------------------
% 6.40/2.29 % (17321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.29 % (17321)Termination reason: Unknown
% 6.40/2.29 % (17321)Termination phase: Saturation
% 6.40/2.29
% 6.40/2.29 % (17321)Memory used [KB]: 6652
% 6.40/2.29 % (17321)Time elapsed: 0.045 s
% 6.40/2.29 % (17321)Instructions burned: 96 (million)
% 6.40/2.29 % (17321)------------------------------
% 6.40/2.29 % (17321)------------------------------
% 6.85/2.30 % (17325)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_17169 for (2993ds/11Mi)
% 6.85/2.30 % (17324)Instruction limit reached!
% 6.85/2.30 % (17324)------------------------------
% 6.85/2.30 % (17324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.30 % (17324)Termination reason: Unknown
% 6.85/2.30 % (17324)Termination phase: Property scanning
% 6.85/2.30
% 6.85/2.30 % (17324)Memory used [KB]: 2046
% 6.85/2.30 % (17324)Time elapsed: 0.038 s
% 6.85/2.30 % (17324)Instructions burned: 84 (million)
% 6.85/2.30 % (17324)------------------------------
% 6.85/2.30 % (17324)------------------------------
% 6.85/2.30 % (17326)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_17169 for (2993ds/41Mi)
% 6.85/2.30 % (17325)Instruction limit reached!
% 6.85/2.30 % (17325)------------------------------
% 6.85/2.30 % (17325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.30 % (17325)Termination reason: Unknown
% 6.85/2.30 % (17325)Termination phase: shuffling
% 6.85/2.30
% 6.85/2.30 % (17325)Memory used [KB]: 1535
% 6.85/2.30 % (17325)Time elapsed: 0.007 s
% 6.85/2.30 % (17325)Instructions burned: 11 (million)
% 6.85/2.30 % (17325)------------------------------
% 6.85/2.30 % (17325)------------------------------
% 6.85/2.32 % (17327)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17169 for (2993ds/6Mi)
% 6.85/2.32 % (17328)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_17169 for (2993ds/150Mi)
% 6.85/2.32 % (17327)Instruction limit reached!
% 6.85/2.32 % (17327)------------------------------
% 6.85/2.32 % (17327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.32 % (17327)Termination reason: Unknown
% 6.85/2.32 % (17327)Termination phase: shuffling
% 6.85/2.32
% 6.85/2.32 % (17327)Memory used [KB]: 1407
% 6.85/2.32 % (17327)Time elapsed: 0.005 s
% 6.85/2.32 % (17327)Instructions burned: 7 (million)
% 6.85/2.32 % (17327)------------------------------
% 6.85/2.32 % (17327)------------------------------
% 6.85/2.32 % (17326)Instruction limit reached!
% 6.85/2.32 % (17326)------------------------------
% 6.85/2.32 % (17326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.32 % (17326)Termination reason: Unknown
% 6.85/2.32 % (17326)Termination phase: Property scanning
% 6.85/2.32
% 6.85/2.32 % (17326)Memory used [KB]: 1918
% 6.85/2.32 % (17326)Time elapsed: 0.020 s
% 6.85/2.32 % (17326)Instructions burned: 41 (million)
% 6.85/2.32 % (17326)------------------------------
% 6.85/2.32 % (17326)------------------------------
% 6.85/2.33 % (17311)Instruction limit reached!
% 6.85/2.33 % (17311)------------------------------
% 6.85/2.33 % (17311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.33 % (17311)Termination reason: Unknown
% 6.85/2.33 % (17311)Termination phase: Saturation
% 6.85/2.33
% 6.85/2.33 % (17311)Memory used [KB]: 7675
% 6.85/2.33 % (17311)Time elapsed: 0.239 s
% 6.85/2.33 % (17311)Instructions burned: 508 (million)
% 6.85/2.33 % (17311)------------------------------
% 6.85/2.33 % (17311)------------------------------
% 6.85/2.34 % (17329)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_17169 for (2993ds/343Mi)
% 6.85/2.34 % (17330)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_17169 for (2993ds/109Mi)
% 6.85/2.35 % (17331)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_17169 for (2993ds/253Mi)
% 6.85/2.37 % (17318)Instruction limit reached!
% 6.85/2.37 % (17318)------------------------------
% 6.85/2.37 % (17318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.37 % (17318)Termination reason: Unknown
% 6.85/2.37 % (17318)Termination phase: Saturation
% 6.85/2.37
% 6.85/2.37 % (17318)Memory used [KB]: 3582
% 6.85/2.37 % (17318)Time elapsed: 0.173 s
% 6.85/2.37 % (17318)Instructions burned: 432 (million)
% 6.85/2.37 % (17318)------------------------------
% 6.85/2.37 % (17318)------------------------------
% 6.85/2.39 % (17330)Instruction limit reached!
% 6.85/2.39 % (17330)------------------------------
% 6.85/2.39 % (17330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.39 % (17332)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_17169 for (2992ds/140Mi)
% 6.85/2.39 % (17330)Termination reason: Unknown
% 6.85/2.39 % (17330)Termination phase: Saturation
% 6.85/2.39
% 6.85/2.39 % (17330)Memory used [KB]: 6652
% 6.85/2.39 % (17330)Time elapsed: 0.049 s
% 6.85/2.39 % (17330)Instructions burned: 109 (million)
% 6.85/2.39 % (17330)------------------------------
% 6.85/2.39 % (17330)------------------------------
% 6.85/2.39 % (17328)Instruction limit reached!
% 6.85/2.39 % (17328)------------------------------
% 6.85/2.39 % (17328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.39 % (17328)Termination reason: Unknown
% 6.85/2.39 % (17328)Termination phase: Saturation
% 6.85/2.39
% 6.85/2.39 % (17328)Memory used [KB]: 8187
% 6.85/2.39 % (17328)Time elapsed: 0.074 s
% 6.85/2.39 % (17328)Instructions burned: 151 (million)
% 6.85/2.39 % (17328)------------------------------
% 6.85/2.39 % (17328)------------------------------
% 7.56/2.40 % (17333)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_17169 for (2992ds/614Mi)
% 7.56/2.41 % (17334)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_17169 for (2992ds/202Mi)
% 7.56/2.42 % (17322)Instruction limit reached!
% 7.56/2.42 % (17322)------------------------------
% 7.56/2.42 % (17322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.42 % (17322)Termination reason: Unknown
% 7.56/2.42 % (17322)Termination phase: Saturation
% 7.56/2.42
% 7.56/2.42 % (17322)Memory used [KB]: 6908
% 7.56/2.42 % (17322)Time elapsed: 0.172 s
% 7.56/2.42 % (17322)Instructions burned: 453 (million)
% 7.56/2.42 % (17322)------------------------------
% 7.56/2.42 % (17322)------------------------------
% 7.56/2.43 % (17335)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_17169 for (2992ds/339Mi)
% 7.56/2.44 % (17332)Instruction limit reached!
% 7.56/2.44 % (17332)------------------------------
% 7.56/2.44 % (17332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.45 % (17332)Termination reason: Unknown
% 7.56/2.45 % (17332)Termination phase: Saturation
% 7.56/2.45
% 7.56/2.45 % (17332)Memory used [KB]: 6908
% 7.56/2.45 % (17332)Time elapsed: 0.060 s
% 7.56/2.45 % (17332)Instructions burned: 140 (million)
% 7.56/2.45 % (17332)------------------------------
% 7.56/2.45 % (17332)------------------------------
% 7.56/2.46 % (17336)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_17169 for (2992ds/283Mi)
% 7.56/2.47 % (17331)Instruction limit reached!
% 7.56/2.47 % (17331)------------------------------
% 7.56/2.47 % (17331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.47 % (17331)Termination reason: Unknown
% 7.56/2.47 % (17331)Termination phase: Saturation
% 7.56/2.47
% 7.56/2.47 % (17331)Memory used [KB]: 8443
% 7.56/2.47 % (17331)Time elapsed: 0.125 s
% 7.56/2.47 % (17331)Instructions burned: 254 (million)
% 7.56/2.47 % (17331)------------------------------
% 7.56/2.47 % (17331)------------------------------
% 7.56/2.49 % (17337)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_17169 for (2991ds/134Mi)
% 7.56/2.49 % (17329)Instruction limit reached!
% 7.56/2.49 % (17329)------------------------------
% 7.56/2.49 % (17329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.49 % (17329)Termination reason: Unknown
% 7.56/2.49 % (17329)Termination phase: Saturation
% 7.56/2.49
% 7.56/2.49 % (17329)Memory used [KB]: 8059
% 7.56/2.49 % (17329)Time elapsed: 0.158 s
% 7.56/2.49 % (17329)Instructions burned: 343 (million)
% 7.56/2.49 % (17329)------------------------------
% 7.56/2.49 % (17329)------------------------------
% 8.15/2.51 % (17334)Instruction limit reached!
% 8.15/2.51 % (17334)------------------------------
% 8.15/2.51 % (17334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.51 % (17334)Termination reason: Unknown
% 8.15/2.51 % (17334)Termination phase: Saturation
% 8.15/2.51
% 8.15/2.51 % (17334)Memory used [KB]: 8955
% 8.15/2.51 % (17334)Time elapsed: 0.101 s
% 8.15/2.51 % (17334)Instructions burned: 203 (million)
% 8.15/2.51 % (17334)------------------------------
% 8.15/2.51 % (17334)------------------------------
% 8.15/2.51 % (17338)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_17169 for (2991ds/298Mi)
% 8.15/2.53 % (17339)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_17169 for (2991ds/192Mi)
% 8.15/2.55 % (17337)Instruction limit reached!
% 8.15/2.55 % (17337)------------------------------
% 8.15/2.55 % (17337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.55 % (17337)Termination reason: Unknown
% 8.15/2.55 % (17337)Termination phase: Saturation
% 8.15/2.55
% 8.15/2.55 % (17337)Memory used [KB]: 7036
% 8.15/2.55 % (17337)Time elapsed: 0.063 s
% 8.15/2.55 % (17337)Instructions burned: 135 (million)
% 8.15/2.55 % (17337)------------------------------
% 8.15/2.55 % (17337)------------------------------
% 8.15/2.57 % (17340)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_17169 for (2990ds/258Mi)
% 8.15/2.57 % (17336)Instruction limit reached!
% 8.15/2.57 % (17336)------------------------------
% 8.15/2.57 % (17336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.57 % (17336)Termination reason: Unknown
% 8.15/2.57 % (17336)Termination phase: Saturation
% 8.15/2.57
% 8.15/2.57 % (17336)Memory used [KB]: 7803
% 8.15/2.57 % (17336)Time elapsed: 0.114 s
% 8.15/2.57 % (17336)Instructions burned: 285 (million)
% 8.15/2.57 % (17336)------------------------------
% 8.15/2.57 % (17336)------------------------------
% 8.15/2.58 % (17335)Instruction limit reached!
% 8.15/2.58 % (17335)------------------------------
% 8.15/2.58 % (17335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.58 % (17335)Termination reason: Unknown
% 8.15/2.58 % (17335)Termination phase: Saturation
% 8.15/2.58
% 8.15/2.58 % (17335)Memory used [KB]: 7675
% 8.15/2.58 % (17335)Time elapsed: 0.150 s
% 8.15/2.58 % (17335)Instructions burned: 340 (million)
% 8.15/2.58 % (17335)------------------------------
% 8.15/2.58 % (17335)------------------------------
% 8.15/2.59 % (17341)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_17169 for (2990ds/90Mi)
% 8.64/2.60 % (17342)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_17169 for (2990ds/231Mi)
% 8.64/2.61 % (17339)Instruction limit reached!
% 8.64/2.61 % (17339)------------------------------
% 8.64/2.61 % (17339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.61 % (17339)Termination reason: Unknown
% 8.64/2.61 % (17339)Termination phase: Saturation
% 8.64/2.61
% 8.64/2.61 % (17339)Memory used [KB]: 7547
% 8.64/2.61 % (17339)Time elapsed: 0.089 s
% 8.64/2.61 % (17339)Instructions burned: 192 (million)
% 8.64/2.61 % (17339)------------------------------
% 8.64/2.61 % (17339)------------------------------
% 8.64/2.63 % (17338)Instruction limit reached!
% 8.64/2.63 % (17338)------------------------------
% 8.64/2.63 % (17338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.63 % (17338)Termination reason: Unknown
% 8.64/2.63 % (17338)Termination phase: Saturation
% 8.64/2.63
% 8.64/2.63 % (17338)Memory used [KB]: 6908
% 8.64/2.63 % (17338)Time elapsed: 0.120 s
% 8.64/2.63 % (17338)Instructions burned: 299 (million)
% 8.64/2.63 % (17338)------------------------------
% 8.64/2.63 % (17338)------------------------------
% 8.64/2.63 % (17341)Instruction limit reached!
% 8.64/2.63 % (17341)------------------------------
% 8.64/2.63 % (17341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.63 % (17341)Termination reason: Unknown
% 8.64/2.63 % (17341)Termination phase: Twee Goal Transformation
% 8.64/2.63
% 8.64/2.63 % (17341)Memory used [KB]: 2558
% 8.64/2.63 % (17341)Time elapsed: 0.040 s
% 8.64/2.63 % (17341)Instructions burned: 90 (million)
% 8.64/2.63 % (17341)------------------------------
% 8.64/2.63 % (17341)------------------------------
% 8.64/2.63 % (17343)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_17169 for (2990ds/458Mi)
% 8.64/2.64 % (17345)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_17169 for (2990ds/297Mi)
% 8.64/2.64 % (17344)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17169 for (2990ds/31Mi)
% 8.64/2.66 % (17344)Instruction limit reached!
% 8.64/2.66 % (17344)------------------------------
% 8.64/2.66 % (17344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.66 % (17344)Termination reason: Unknown
% 8.64/2.66 % (17344)Termination phase: Property scanning
% 8.64/2.66
% 8.64/2.66 % (17344)Memory used [KB]: 1918
% 8.64/2.66 % (17344)Time elapsed: 0.016 s
% 8.64/2.66 % (17344)Instructions burned: 32 (million)
% 8.64/2.66 % (17344)------------------------------
% 8.64/2.66 % (17344)------------------------------
% 8.64/2.67 % (17346)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_17169 for (2989ds/987Mi)
% 8.64/2.69 % (17340)Instruction limit reached!
% 8.64/2.69 % (17340)------------------------------
% 8.64/2.69 % (17340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.69 % (17340)Termination reason: Unknown
% 8.64/2.69 % (17340)Termination phase: Saturation
% 8.64/2.69
% 8.64/2.69 % (17340)Memory used [KB]: 7803
% 8.64/2.69 % (17340)Time elapsed: 0.119 s
% 8.64/2.69 % (17340)Instructions burned: 258 (million)
% 8.64/2.69 % (17340)------------------------------
% 8.64/2.69 % (17340)------------------------------
% 9.10/2.70 % (17333)Instruction limit reached!
% 9.10/2.70 % (17333)------------------------------
% 9.10/2.70 % (17333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.10/2.70 % (17333)Termination reason: Unknown
% 9.10/2.70 % (17333)Termination phase: Saturation
% 9.10/2.70
% 9.10/2.70 % (17333)Memory used [KB]: 8571
% 9.10/2.70 % (17333)Time elapsed: 0.297 s
% 9.10/2.70 % (17333)Instructions burned: 615 (million)
% 9.10/2.70 % (17333)------------------------------
% 9.10/2.70 % (17333)------------------------------
% 9.10/2.70 % (17347)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_17169 for (2989ds/182Mi)
% 9.10/2.71 % (17342)Instruction limit reached!
% 9.10/2.71 % (17342)------------------------------
% 9.10/2.71 % (17342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.10/2.71 % (17342)Termination reason: Unknown
% 9.10/2.71 % (17342)Termination phase: Saturation
% 9.10/2.71
% 9.10/2.71 % (17342)Memory used [KB]: 12281
% 9.10/2.71 % (17342)Time elapsed: 0.134 s
% 9.10/2.71 % (17342)Instructions burned: 231 (million)
% 9.10/2.71 % (17342)------------------------------
% 9.10/2.71 % (17342)------------------------------
% 9.10/2.71 % (17315)Instruction limit reached!
% 9.10/2.71 % (17315)------------------------------
% 9.10/2.71 % (17315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.10/2.71 % (17315)Termination reason: Unknown
% 9.10/2.71 % (17315)Termination phase: Saturation
% 9.10/2.71
% 9.10/2.71 % (17315)Memory used [KB]: 10874
% 9.10/2.71 % (17315)Time elapsed: 0.554 s
% 9.10/2.71 % (17315)Instructions burned: 1087 (million)
% 9.10/2.71 % (17315)------------------------------
% 9.10/2.71 % (17315)------------------------------
% 9.10/2.71 % (17348)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_17169 for (2989ds/182Mi)
% 9.10/2.72 % (17349)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_17169 for (2989ds/154Mi)
% 9.10/2.73 % (17350)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_17169 for (2989ds/79Mi)
% 9.10/2.76 % (17345)Instruction limit reached!
% 9.10/2.76 % (17345)------------------------------
% 9.10/2.76 % (17345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.10/2.76 % (17345)Termination reason: Unknown
% 9.10/2.76 % (17345)Termination phase: Saturation
% 9.10/2.76
% 9.10/2.76 % (17345)Memory used [KB]: 7419
% 9.10/2.76 % (17345)Time elapsed: 0.117 s
% 9.10/2.76 % (17345)Instructions burned: 298 (million)
% 9.10/2.76 % (17345)------------------------------
% 9.10/2.76 % (17345)------------------------------
% 9.10/2.76 % (17350)Instruction limit reached!
% 9.10/2.76 % (17350)------------------------------
% 9.10/2.76 % (17350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.10/2.76 % (17350)Termination reason: Unknown
% 9.10/2.76 % (17350)Termination phase: Property scanning
% 9.10/2.76
% 9.10/2.76 % (17350)Memory used [KB]: 2174
% 9.10/2.76 % (17350)Time elapsed: 0.038 s
% 9.10/2.76 % (17350)Instructions burned: 81 (million)
% 9.10/2.76 % (17350)------------------------------
% 9.10/2.76 % (17350)------------------------------
% 9.10/2.77 % (17351)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_17169 for (2988ds/216Mi)
% 9.10/2.78 % (17352)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_17169 for (2988ds/114Mi)
% 9.10/2.78 % (17347)Instruction limit reached!
% 9.10/2.78 % (17347)------------------------------
% 9.10/2.78 % (17347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.10/2.78 % (17347)Termination reason: Unknown
% 9.10/2.78 % (17347)Termination phase: Saturation
% 9.10/2.78
% 9.10/2.78 % (17347)Memory used [KB]: 7419
% 9.10/2.78 % (17347)Time elapsed: 0.082 s
% 9.10/2.78 % (17347)Instructions burned: 182 (million)
% 9.10/2.78 % (17347)------------------------------
% 9.10/2.78 % (17347)------------------------------
% 9.10/2.79 % (17349)Instruction limit reached!
% 9.10/2.79 % (17349)------------------------------
% 9.10/2.79 % (17349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.10/2.79 % (17349)Termination reason: Unknown
% 9.10/2.79 % (17349)Termination phase: Saturation
% 9.10/2.79
% 9.10/2.79 % (17349)Memory used [KB]: 6780
% 9.10/2.79 % (17349)Time elapsed: 0.067 s
% 9.10/2.79 % (17349)Instructions burned: 156 (million)
% 9.10/2.79 % (17349)------------------------------
% 9.10/2.79 % (17349)------------------------------
% 10.46/2.80 % (17353)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_17169 for (2988ds/922Mi)
% 10.46/2.80 % (17348)Instruction limit reached!
% 10.46/2.80 % (17348)------------------------------
% 10.46/2.80 % (17348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.80 % (17348)Termination reason: Unknown
% 10.46/2.80 % (17348)Termination phase: Saturation
% 10.46/2.80
% 10.46/2.80 % (17348)Memory used [KB]: 10106
% 10.46/2.80 % (17348)Time elapsed: 0.088 s
% 10.46/2.80 % (17348)Instructions burned: 182 (million)
% 10.46/2.80 % (17348)------------------------------
% 10.46/2.80 % (17348)------------------------------
% 10.46/2.80 % (17354)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_17169 for (2988ds/182Mi)
% 10.46/2.82 % (17355)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_17169 for (2988ds/164Mi)
% 10.46/2.83 % (17352)Instruction limit reached!
% 10.46/2.83 % (17352)------------------------------
% 10.46/2.83 % (17352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.83 % (17352)Termination reason: Unknown
% 10.46/2.83 % (17352)Termination phase: Saturation
% 10.46/2.83
% 10.46/2.83 % (17352)Memory used [KB]: 6908
% 10.46/2.83 % (17352)Time elapsed: 0.054 s
% 10.46/2.83 % (17352)Instructions burned: 115 (million)
% 10.46/2.83 % (17352)------------------------------
% 10.46/2.83 % (17352)------------------------------
% 10.46/2.85 % (17356)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_17169 for (2988ds/50Mi)
% 10.46/2.85 % (17343)Instruction limit reached!
% 10.46/2.85 % (17343)------------------------------
% 10.46/2.85 % (17343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.85 % (17343)Termination reason: Unknown
% 10.46/2.85 % (17343)Termination phase: Saturation
% 10.46/2.85
% 10.46/2.85 % (17343)Memory used [KB]: 8315
% 10.46/2.85 % (17343)Time elapsed: 0.220 s
% 10.46/2.85 % (17343)Instructions burned: 458 (million)
% 10.46/2.85 % (17343)------------------------------
% 10.46/2.85 % (17343)------------------------------
% 10.46/2.86 % (17351)Instruction limit reached!
% 10.46/2.86 % (17351)------------------------------
% 10.46/2.86 % (17351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.86 % (17351)Termination reason: Unknown
% 10.46/2.86 % (17351)Termination phase: Saturation
% 10.46/2.86
% 10.46/2.86 % (17351)Memory used [KB]: 6908
% 10.46/2.86 % (17351)Time elapsed: 0.088 s
% 10.46/2.86 % (17351)Instructions burned: 217 (million)
% 10.46/2.86 % (17351)------------------------------
% 10.46/2.86 % (17351)------------------------------
% 10.46/2.87 % (17357)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_17169 for (2987ds/368Mi)
% 10.46/2.87 % (17356)Instruction limit reached!
% 10.46/2.87 % (17356)------------------------------
% 10.46/2.87 % (17356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.87 % (17356)Termination reason: Unknown
% 10.46/2.87 % (17356)Termination phase: Property scanning
% 10.46/2.87
% 10.46/2.87 % (17356)Memory used [KB]: 2046
% 10.46/2.87 % (17356)Time elapsed: 0.024 s
% 10.46/2.87 % (17356)Instructions burned: 50 (million)
% 10.46/2.87 % (17356)------------------------------
% 10.46/2.87 % (17356)------------------------------
% 10.46/2.88 % (17358)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_17169 for (2987ds/1021Mi)
% 10.46/2.88 % (17354)Instruction limit reached!
% 10.46/2.88 % (17354)------------------------------
% 10.46/2.88 % (17354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.88 % (17354)Termination reason: Unknown
% 10.46/2.88 % (17354)Termination phase: Saturation
% 10.46/2.88
% 10.46/2.88 % (17354)Memory used [KB]: 6780
% 10.46/2.88 % (17354)Time elapsed: 0.078 s
% 10.46/2.88 % (17354)Instructions burned: 182 (million)
% 10.46/2.88 % (17354)------------------------------
% 10.46/2.88 % (17354)------------------------------
% 10.46/2.89 % (17359)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_17169 for (2987ds/267Mi)
% 10.46/2.89 % (17355)Instruction limit reached!
% 10.46/2.89 % (17355)------------------------------
% 10.46/2.89 % (17355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.89 % (17355)Termination reason: Unknown
% 10.46/2.89 % (17355)Termination phase: Saturation
% 10.46/2.89
% 10.46/2.89 % (17355)Memory used [KB]: 2430
% 10.46/2.89 % (17355)Time elapsed: 0.073 s
% 10.46/2.89 % (17355)Instructions burned: 164 (million)
% 10.46/2.89 % (17355)------------------------------
% 10.46/2.89 % (17355)------------------------------
% 11.18/2.90 % (17360)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_17169 for (2987ds/204Mi)
% 11.18/2.91 % (17361)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17169 for (2987ds/26Mi)
% 11.18/2.92 % (17361)Instruction limit reached!
% 11.18/2.92 % (17361)------------------------------
% 11.18/2.92 % (17361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.18/2.92 % (17361)Termination reason: Unknown
% 11.18/2.92 % (17361)Termination phase: shuffling
% 11.18/2.92
% 11.18/2.92 % (17361)Memory used [KB]: 1918
% 11.18/2.92 % (17361)Time elapsed: 0.013 s
% 11.18/2.92 % (17361)Instructions burned: 26 (million)
% 11.18/2.92 % (17361)------------------------------
% 11.18/2.92 % (17361)------------------------------
% 11.18/2.93 % (17362)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_17169 for (2987ds/53Mi)
% 11.18/2.96 % (17362)Instruction limit reached!
% 11.18/2.96 % (17362)------------------------------
% 11.18/2.96 % (17362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.18/2.96 % (17362)Termination reason: Unknown
% 11.18/2.96 % (17362)Termination phase: Property scanning
% 11.18/2.96
% 11.18/2.96 % (17362)Memory used [KB]: 2046
% 11.18/2.96 % (17362)Time elapsed: 0.025 s
% 11.18/2.96 % (17362)Instructions burned: 55 (million)
% 11.18/2.96 % (17362)------------------------------
% 11.18/2.96 % (17362)------------------------------
% 11.18/2.97 % (17363)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_17169 for (2986ds/4436Mi)
% 11.18/2.99 % (17360)Instruction limit reached!
% 11.18/2.99 % (17360)------------------------------
% 11.18/2.99 % (17360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.18/2.99 % (17360)Termination reason: Unknown
% 11.18/2.99 % (17360)Termination phase: Saturation
% 11.18/2.99
% 11.18/2.99 % (17360)Memory used [KB]: 7547
% 11.18/2.99 % (17360)Time elapsed: 0.093 s
% 11.18/2.99 % (17360)Instructions burned: 206 (million)
% 11.18/2.99 % (17360)------------------------------
% 11.18/2.99 % (17360)------------------------------
% 11.18/3.00 % (17359)Instruction limit reached!
% 11.18/3.00 % (17359)------------------------------
% 11.18/3.00 % (17359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.18/3.00 % (17359)Termination reason: Unknown
% 11.18/3.00 % (17359)Termination phase: Saturation
% 11.18/3.00
% 11.18/3.00 % (17359)Memory used [KB]: 6908
% 11.18/3.00 % (17359)Time elapsed: 0.112 s
% 11.18/3.00 % (17359)Instructions burned: 269 (million)
% 11.18/3.00 % (17359)------------------------------
% 11.18/3.00 % (17359)------------------------------
% 11.18/3.01 % (17364)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_17169 for (2986ds/1539Mi)
% 11.18/3.02 % (17365)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_17169 for (2986ds/408Mi)
% 12.49/3.04 % (17357)Instruction limit reached!
% 12.49/3.04 % (17357)------------------------------
% 12.49/3.04 % (17357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.49/3.04 % (17357)Termination reason: Unknown
% 12.49/3.04 % (17357)Termination phase: Saturation
% 12.49/3.04
% 12.49/3.04 % (17357)Memory used [KB]: 8187
% 12.49/3.04 % (17357)Time elapsed: 0.178 s
% 12.49/3.04 % (17357)Instructions burned: 369 (million)
% 12.49/3.04 % (17357)------------------------------
% 12.49/3.04 % (17357)------------------------------
% 12.49/3.06 % (17366)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_17169 for (2985ds/5205Mi)
% 13.03/3.16 % (17346)Instruction limit reached!
% 13.03/3.16 % (17346)------------------------------
% 13.03/3.16 % (17346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.16 % (17346)Termination reason: Unknown
% 13.03/3.16 % (17346)Termination phase: Saturation
% 13.03/3.16
% 13.03/3.16 % (17346)Memory used [KB]: 10618
% 13.03/3.16 % (17346)Time elapsed: 0.485 s
% 13.03/3.16 % (17346)Instructions burned: 987 (million)
% 13.03/3.16 % (17346)------------------------------
% 13.03/3.16 % (17346)------------------------------
% 13.03/3.17 % (17367)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_17169 for (2984ds/1913Mi)
% 13.33/3.21 % (17365)Instruction limit reached!
% 13.33/3.21 % (17365)------------------------------
% 13.33/3.21 % (17365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.21 % (17365)Termination reason: Unknown
% 13.33/3.21 % (17365)Termination phase: Saturation
% 13.33/3.21
% 13.33/3.21 % (17365)Memory used [KB]: 9338
% 13.33/3.21 % (17365)Time elapsed: 0.201 s
% 13.33/3.21 % (17365)Instructions burned: 408 (million)
% 13.33/3.21 % (17365)------------------------------
% 13.33/3.21 % (17365)------------------------------
% 13.33/3.23 % (17368)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_17169 for (2984ds/4350Mi)
% 13.33/3.26 % (17353)Instruction limit reached!
% 13.33/3.26 % (17353)------------------------------
% 13.33/3.26 % (17353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.26 % (17353)Termination reason: Unknown
% 13.33/3.26 % (17353)Termination phase: Saturation
% 13.33/3.26
% 13.33/3.26 % (17353)Memory used [KB]: 9978
% 13.33/3.26 % (17353)Time elapsed: 0.459 s
% 13.33/3.26 % (17353)Instructions burned: 922 (million)
% 13.33/3.26 % (17353)------------------------------
% 13.33/3.26 % (17353)------------------------------
% 13.33/3.28 % (17369)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_17169 for (2983ds/68Mi)
% 13.92/3.31 % (17369)Instruction limit reached!
% 13.92/3.31 % (17369)------------------------------
% 13.92/3.31 % (17369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.31 % (17369)Termination reason: Unknown
% 13.92/3.31 % (17369)Termination phase: Property scanning
% 13.92/3.31
% 13.92/3.31 % (17369)Memory used [KB]: 2046
% 13.92/3.31 % (17369)Time elapsed: 0.032 s
% 13.92/3.31 % (17369)Instructions burned: 69 (million)
% 13.92/3.31 % (17369)------------------------------
% 13.92/3.31 % (17369)------------------------------
% 13.92/3.32 % (17370)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_17169 for (2983ds/358Mi)
% 13.92/3.39 % (17358)Instruction limit reached!
% 13.92/3.39 % (17358)------------------------------
% 13.92/3.39 % (17358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.39 % (17358)Termination reason: Unknown
% 13.92/3.39 % (17358)Termination phase: Saturation
% 13.92/3.39
% 13.92/3.39 % (17358)Memory used [KB]: 10618
% 13.92/3.39 % (17358)Time elapsed: 0.512 s
% 13.92/3.39 % (17358)Instructions burned: 1022 (million)
% 13.92/3.39 % (17358)------------------------------
% 13.92/3.39 % (17358)------------------------------
% 14.26/3.41 % (17371)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17169 for (2982ds/31Mi)
% 14.26/3.42 % (17371)Instruction limit reached!
% 14.26/3.42 % (17371)------------------------------
% 14.26/3.42 % (17371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.26/3.42 % (17371)Termination reason: Unknown
% 14.26/3.42 % (17371)Termination phase: Property scanning
% 14.26/3.42
% 14.26/3.42 % (17371)Memory used [KB]: 1918
% 14.26/3.42 % (17371)Time elapsed: 0.015 s
% 14.26/3.42 % (17371)Instructions burned: 31 (million)
% 14.26/3.42 % (17371)------------------------------
% 14.26/3.42 % (17371)------------------------------
% 14.26/3.44 % (17372)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_17169 for (2982ds/279Mi)
% 14.26/3.49 % (17370)Instruction limit reached!
% 14.26/3.49 % (17370)------------------------------
% 14.26/3.49 % (17370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.26/3.49 % (17370)Termination reason: Unknown
% 14.26/3.49 % (17370)Termination phase: Saturation
% 14.26/3.49
% 14.26/3.49 % (17370)Memory used [KB]: 7931
% 14.26/3.49 % (17370)Time elapsed: 0.167 s
% 14.26/3.49 % (17370)Instructions burned: 359 (million)
% 14.26/3.49 % (17370)------------------------------
% 14.26/3.49 % (17370)------------------------------
% 14.68/3.51 % (17373)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_17169 for (2981ds/258Mi)
% 14.68/3.53 % (17364)Instruction limit reached!
% 14.68/3.53 % (17364)------------------------------
% 14.68/3.53 % (17364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.68/3.53 % (17364)Termination reason: Unknown
% 14.68/3.53 % (17364)Termination phase: Saturation
% 14.68/3.53
% 14.68/3.53 % (17364)Memory used [KB]: 8315
% 14.68/3.53 % (17364)Time elapsed: 0.529 s
% 14.68/3.53 % (17364)Instructions burned: 1541 (million)
% 14.68/3.53 % (17364)------------------------------
% 14.68/3.53 % (17364)------------------------------
% 14.68/3.55 % (17372)Instruction limit reached!
% 14.68/3.55 % (17372)------------------------------
% 14.68/3.55 % (17372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.68/3.55 % (17372)Termination reason: Unknown
% 14.68/3.55 % (17372)Termination phase: Saturation
% 14.68/3.55
% 14.68/3.55 % (17372)Memory used [KB]: 6908
% 14.68/3.55 % (17372)Time elapsed: 0.115 s
% 14.68/3.55 % (17372)Instructions burned: 280 (million)
% 14.68/3.55 % (17372)------------------------------
% 14.68/3.55 % (17372)------------------------------
% 14.68/3.55 % (17374)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17169 for (2981ds/26Mi)
% 14.68/3.56 % (17374)Instruction limit reached!
% 14.68/3.56 % (17374)------------------------------
% 14.68/3.56 % (17374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.68/3.56 % (17374)Termination reason: Unknown
% 14.68/3.56 % (17374)Termination phase: shuffling
% 14.68/3.56
% 14.68/3.56 % (17374)Memory used [KB]: 1918
% 14.68/3.56 % (17374)Time elapsed: 0.014 s
% 14.68/3.56 % (17374)Instructions burned: 27 (million)
% 14.68/3.56 % (17374)------------------------------
% 14.68/3.56 % (17374)------------------------------
% 14.68/3.57 % (17375)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_17169 for (2980ds/995Mi)
% 14.68/3.58 % (17376)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_17169 for (2980ds/373Mi)
% 14.98/3.62 % (17373)Instruction limit reached!
% 14.98/3.62 % (17373)------------------------------
% 14.98/3.62 % (17373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.98/3.62 % (17373)Termination reason: Unknown
% 14.98/3.62 % (17373)Termination phase: Saturation
% 14.98/3.62
% 14.98/3.62 % (17373)Memory used [KB]: 8315
% 14.98/3.62 % (17373)Time elapsed: 0.115 s
% 14.98/3.62 % (17373)Instructions burned: 259 (million)
% 14.98/3.62 % (17373)------------------------------
% 14.98/3.62 % (17373)------------------------------
% 14.98/3.64 % (17377)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_17169 for (2980ds/253Mi)
% 15.21/3.74 % (17377)Instruction limit reached!
% 15.21/3.74 % (17377)------------------------------
% 15.21/3.74 % (17377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.21/3.74 % (17377)Termination reason: Unknown
% 15.21/3.74 % (17377)Termination phase: Saturation
% 15.21/3.74
% 15.21/3.74 % (17377)Memory used [KB]: 7036
% 15.21/3.74 % (17377)Time elapsed: 0.106 s
% 15.21/3.74 % (17377)Instructions burned: 254 (million)
% 15.21/3.74 % (17377)------------------------------
% 15.21/3.74 % (17377)------------------------------
% 15.21/3.76 % (17376)Instruction limit reached!
% 15.21/3.76 % (17376)------------------------------
% 15.21/3.76 % (17376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.21/3.76 % (17376)Termination reason: Unknown
% 15.21/3.76 % (17376)Termination phase: Saturation
% 15.21/3.76
% 15.21/3.76 % (17376)Memory used [KB]: 8059
% 15.21/3.76 % (17376)Time elapsed: 0.203 s
% 15.21/3.76 % (17376)Instructions burned: 374 (million)
% 15.21/3.76 % (17376)------------------------------
% 15.21/3.76 % (17376)------------------------------
% 15.21/3.76 % (17378)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_17169 for (2978ds/832Mi)
% 15.21/3.77 % (17379)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_17169 for (2978ds/668Mi)
% 15.73/3.94 % (17375)Instruction limit reached!
% 15.73/3.94 % (17375)------------------------------
% 15.73/3.94 % (17375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.73/3.94 % (17375)Termination reason: Unknown
% 15.73/3.94 % (17375)Termination phase: Saturation
% 15.73/3.94
% 15.73/3.94 % (17375)Memory used [KB]: 10746
% 15.73/3.94 % (17375)Time elapsed: 0.372 s
% 15.73/3.94 % (17375)Instructions burned: 995 (million)
% 15.73/3.94 % (17375)------------------------------
% 15.73/3.94 % (17375)------------------------------
% 15.73/3.95 % (17380)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_17169 for (2976ds/40Mi)
% 15.73/3.97 % (17380)Instruction limit reached!
% 15.73/3.97 % (17380)------------------------------
% 15.73/3.97 % (17380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.73/3.97 % (17380)Termination reason: Unknown
% 15.73/3.97 % (17380)Termination phase: Property scanning
% 15.73/3.97
% 15.73/3.97 % (17380)Memory used [KB]: 1918
% 15.73/3.97 % (17380)Time elapsed: 0.020 s
% 15.73/3.97 % (17380)Instructions burned: 41 (million)
% 15.73/3.97 % (17380)------------------------------
% 15.73/3.97 % (17380)------------------------------
% 15.73/3.99 % (17381)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_17169 for (2976ds/294Mi)
% 15.73/4.03 % (17379)Instruction limit reached!
% 15.73/4.03 % (17379)------------------------------
% 15.73/4.03 % (17379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.73/4.03 % (17379)Termination reason: Unknown
% 15.73/4.03 % (17379)Termination phase: Saturation
% 15.73/4.03
% 15.73/4.03 % (17379)Memory used [KB]: 15351
% 15.73/4.03 % (17379)Time elapsed: 0.259 s
% 15.73/4.03 % (17379)Instructions burned: 669 (million)
% 15.73/4.03 % (17379)------------------------------
% 15.73/4.03 % (17379)------------------------------
% 19.23/4.05 % (17382)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_17169 for (2976ds/187Mi)
% 19.23/4.08 % (17367)Instruction limit reached!
% 19.23/4.08 % (17367)------------------------------
% 19.23/4.08 % (17367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.23/4.08 % (17367)Termination reason: Unknown
% 19.23/4.08 % (17367)Termination phase: Saturation
% 19.23/4.08
% 19.23/4.08 % (17367)Memory used [KB]: 4605
% 19.23/4.08 % (17367)Time elapsed: 0.909 s
% 19.23/4.08 % (17367)Instructions burned: 1914 (million)
% 19.23/4.08 % (17367)------------------------------
% 19.23/4.08 % (17367)------------------------------
% 19.23/4.10 % (17383)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_17169 for (2975ds/371Mi)
% 19.23/4.13 % (17382)Instruction limit reached!
% 19.23/4.13 % (17382)------------------------------
% 19.23/4.13 % (17382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.23/4.13 % (17382)Termination reason: Unknown
% 19.23/4.13 % (17382)Termination phase: Saturation
% 19.23/4.13
% 19.23/4.13 % (17382)Memory used [KB]: 7547
% 19.23/4.13 % (17382)Time elapsed: 0.082 s
% 19.23/4.13 % (17382)Instructions burned: 187 (million)
% 19.23/4.13 % (17382)------------------------------
% 19.23/4.13 % (17382)------------------------------
% 20.17/4.13 % (17381)Instruction limit reached!
% 20.17/4.13 % (17381)------------------------------
% 20.17/4.13 % (17381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.17/4.13 % (17381)Termination reason: Unknown
% 20.17/4.13 % (17381)Termination phase: Saturation
% 20.17/4.13
% 20.17/4.13 % (17381)Memory used [KB]: 6908
% 20.17/4.13 % (17381)Time elapsed: 0.125 s
% 20.17/4.13 % (17381)Instructions burned: 294 (million)
% 20.17/4.13 % (17381)------------------------------
% 20.17/4.13 % (17381)------------------------------
% 20.17/4.14 % (17384)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_17169 for (2975ds/1827Mi)
% 20.17/4.15 % (17385)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_17169 for (2974ds/70Mi)
% 20.17/4.16 % (17378)Instruction limit reached!
% 20.17/4.16 % (17378)------------------------------
% 20.17/4.16 % (17378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.17/4.16 % (17378)Termination reason: Unknown
% 20.17/4.16 % (17378)Termination phase: Saturation
% 20.17/4.16
% 20.17/4.16 % (17378)Memory used [KB]: 9594
% 20.17/4.16 % (17378)Time elapsed: 0.401 s
% 20.17/4.16 % (17378)Instructions burned: 833 (million)
% 20.17/4.16 % (17378)------------------------------
% 20.17/4.16 % (17378)------------------------------
% 20.17/4.17 % (17386)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_17169 for (2974ds/316Mi)
% 20.17/4.18 % (17385)Instruction limit reached!
% 20.17/4.18 % (17385)------------------------------
% 20.17/4.18 % (17385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.17/4.18 % (17385)Termination reason: Unknown
% 20.17/4.18 % (17385)Termination phase: Function definition elimination
% 20.17/4.18
% 20.17/4.18 % (17385)Memory used [KB]: 2046
% 20.17/4.18 % (17385)Time elapsed: 0.031 s
% 20.17/4.18 % (17385)Instructions burned: 70 (million)
% 20.17/4.18 % (17385)------------------------------
% 20.17/4.18 % (17385)------------------------------
% 20.17/4.20 % (17387)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_17169 for (2974ds/932Mi)
% 20.45/4.28 % (17383)Instruction limit reached!
% 20.45/4.28 % (17383)------------------------------
% 20.45/4.28 % (17383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.45/4.28 % (17383)Termination reason: Unknown
% 20.45/4.28 % (17383)Termination phase: Saturation
% 20.45/4.28
% 20.45/4.28 % (17383)Memory used [KB]: 8187
% 20.45/4.28 % (17383)Time elapsed: 0.180 s
% 20.45/4.28 % (17383)Instructions burned: 372 (million)
% 20.45/4.28 % (17383)------------------------------
% 20.45/4.28 % (17383)------------------------------
% 20.45/4.29 % (17388)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_17169 for (2973ds/4714Mi)
% 20.94/4.30 % (17386)Instruction limit reached!
% 20.94/4.30 % (17386)------------------------------
% 20.94/4.30 % (17386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.30 % (17386)Termination reason: Unknown
% 20.94/4.30 % (17386)Termination phase: Saturation
% 20.94/4.30
% 20.94/4.30 % (17386)Memory used [KB]: 7164
% 20.94/4.30 % (17386)Time elapsed: 0.128 s
% 20.94/4.30 % (17386)Instructions burned: 316 (million)
% 20.94/4.30 % (17386)------------------------------
% 20.94/4.30 % (17386)------------------------------
% 20.94/4.32 % (17389)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_17169 for (2973ds/8250Mi)
% 21.69/4.56 % (17387)Instruction limit reached!
% 21.69/4.56 % (17387)------------------------------
% 21.69/4.56 % (17387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.69/4.56 % (17387)Termination reason: Unknown
% 21.69/4.56 % (17387)Termination phase: Saturation
% 21.69/4.56
% 21.69/4.56 % (17387)Memory used [KB]: 12025
% 21.69/4.56 % (17387)Time elapsed: 0.370 s
% 21.69/4.56 % (17387)Instructions burned: 934 (million)
% 21.69/4.56 % (17387)------------------------------
% 21.69/4.56 % (17387)------------------------------
% 21.69/4.58 % (17390)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_17169 for (2970ds/770Mi)
% 23.27/4.93 % (17390)Instruction limit reached!
% 23.27/4.93 % (17390)------------------------------
% 23.27/4.93 % (17390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.27/4.93 % (17390)Termination reason: Unknown
% 23.27/4.93 % (17390)Termination phase: Saturation
% 23.27/4.93
% 23.27/4.93 % (17390)Memory used [KB]: 7036
% 23.27/4.93 % (17390)Time elapsed: 0.348 s
% 23.27/4.93 % (17390)Instructions burned: 771 (million)
% 23.27/4.93 % (17390)------------------------------
% 23.27/4.93 % (17390)------------------------------
% 23.27/4.95 % (17391)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_17169 for (2967ds/794Mi)
% 23.27/5.00 % (17384)Instruction limit reached!
% 23.27/5.00 % (17384)------------------------------
% 23.27/5.00 % (17384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.27/5.00 % (17384)Termination reason: Unknown
% 23.27/5.00 % (17384)Termination phase: Saturation
% 23.27/5.00
% 23.27/5.00 % (17384)Memory used [KB]: 17782
% 23.27/5.00 % (17384)Time elapsed: 0.860 s
% 23.27/5.00 % (17384)Instructions burned: 1828 (million)
% 23.27/5.00 % (17384)------------------------------
% 23.27/5.00 % (17384)------------------------------
% 23.27/5.01 % (17366)Instruction limit reached!
% 23.27/5.01 % (17366)------------------------------
% 23.27/5.01 % (17366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.27/5.01 % (17366)Termination reason: Unknown
% 23.27/5.01 % (17366)Termination phase: Saturation
% 23.27/5.01
% 23.27/5.01 % (17366)Memory used [KB]: 11641
% 23.27/5.01 % (17366)Time elapsed: 1.952 s
% 23.27/5.01 % (17366)Instructions burned: 5207 (million)
% 23.27/5.01 % (17366)------------------------------
% 23.27/5.01 % (17366)------------------------------
% 23.27/5.02 % (17392)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_17169 for (2966ds/464Mi)
% 26.41/5.03 % (17393)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_17169 for (2966ds/1376Mi)
% 27.28/5.24 % (17392)Instruction limit reached!
% 27.28/5.24 % (17392)------------------------------
% 27.28/5.24 % (17392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.28/5.24 % (17392)Termination reason: Unknown
% 27.28/5.24 % (17392)Termination phase: Saturation
% 27.28/5.24
% 27.28/5.24 % (17392)Memory used [KB]: 8315
% 27.28/5.24 % (17392)Time elapsed: 0.219 s
% 27.28/5.24 % (17392)Instructions burned: 464 (million)
% 27.28/5.24 % (17392)------------------------------
% 27.28/5.24 % (17392)------------------------------
% 27.28/5.25 % (17394)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_17169 for (2964ds/906Mi)
% 28.02/5.34 % (17391)Instruction limit reached!
% 28.02/5.34 % (17391)------------------------------
% 28.02/5.34 % (17391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.02/5.34 % (17391)Termination reason: Unknown
% 28.02/5.34 % (17391)Termination phase: Saturation
% 28.02/5.34
% 28.02/5.34 % (17391)Memory used [KB]: 4477
% 28.02/5.34 % (17391)Time elapsed: 0.391 s
% 28.02/5.34 % (17391)Instructions burned: 796 (million)
% 28.02/5.34 % (17391)------------------------------
% 28.02/5.34 % (17391)------------------------------
% 28.02/5.35 % (17395)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_17169 for (2963ds/434Mi)
% 28.02/5.36 % (17368)Instruction limit reached!
% 28.02/5.36 % (17368)------------------------------
% 28.02/5.36 % (17368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.02/5.36 % (17368)Termination reason: Unknown
% 28.02/5.36 % (17368)Termination phase: Saturation
% 28.02/5.36
% 28.02/5.36 % (17368)Memory used [KB]: 11385
% 28.02/5.36 % (17368)Time elapsed: 2.132 s
% 28.02/5.36 % (17368)Instructions burned: 4350 (million)
% 28.02/5.36 % (17368)------------------------------
% 28.02/5.36 % (17368)------------------------------
% 28.02/5.38 % (17396)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_17169 for (2962ds/865Mi)
% 28.45/5.40 % (17363)Instruction limit reached!
% 28.45/5.40 % (17363)------------------------------
% 28.45/5.40 % (17363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.45/5.40 % (17363)Termination reason: Unknown
% 28.45/5.40 % (17363)Termination phase: Saturation
% 28.45/5.40
% 28.45/5.40 % (17363)Memory used [KB]: 17014
% 28.45/5.40 % (17363)Time elapsed: 2.444 s
% 28.45/5.40 % (17363)Instructions burned: 4436 (million)
% 28.45/5.40 % (17363)------------------------------
% 28.45/5.40 % (17363)------------------------------
% 28.45/5.42 % (17397)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_17169 for (2962ds/593Mi)
% 28.67/5.55 % (17395)Refutation not found, non-redundant clauses discarded% (17395)------------------------------
% 28.67/5.55 % (17395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.67/5.55 % (17395)Termination reason: Refutation not found, non-redundant clauses discarded
% 28.67/5.55
% 28.67/5.55 % (17395)Memory used [KB]: 9210
% 28.67/5.55 % (17395)Time elapsed: 0.200 s
% 28.67/5.55 % (17395)Instructions burned: 407 (million)
% 28.67/5.55 % (17395)------------------------------
% 28.67/5.55 % (17395)------------------------------
% 28.67/5.57 % (17398)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_17169 for (2960ds/443Mi)
% 28.67/5.58 % (17393)Instruction limit reached!
% 28.67/5.58 % (17393)------------------------------
% 28.67/5.58 % (17393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.67/5.58 % (17393)Termination reason: Unknown
% 28.67/5.58 % (17393)Termination phase: Saturation
% 28.67/5.58
% 28.67/5.58 % (17393)Memory used [KB]: 8443
% 28.67/5.58 % (17393)Time elapsed: 0.551 s
% 28.67/5.58 % (17393)Instructions burned: 1377 (million)
% 28.67/5.58 % (17393)------------------------------
% 28.67/5.58 % (17393)------------------------------
% 28.67/5.60 % (17399)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_17169 for (2960ds/594Mi)
% 29.65/5.65 % (17397)Instruction limit reached!
% 29.65/5.65 % (17397)------------------------------
% 29.65/5.65 % (17397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.65/5.65 % (17397)Termination reason: Unknown
% 29.65/5.65 % (17397)Termination phase: Saturation
% 29.65/5.65
% 29.65/5.65 % (17397)Memory used [KB]: 6908
% 29.65/5.65 % (17397)Time elapsed: 0.226 s
% 29.65/5.65 % (17397)Instructions burned: 594 (million)
% 29.65/5.65 % (17397)------------------------------
% 29.65/5.65 % (17397)------------------------------
% 29.65/5.66 % (17400)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_17169 for (2959ds/327Mi)
% 30.09/5.70 % (17394)Instruction limit reached!
% 30.09/5.70 % (17394)------------------------------
% 30.09/5.70 % (17394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.09/5.70 % (17394)Termination reason: Unknown
% 30.09/5.70 % (17394)Termination phase: Saturation
% 30.09/5.70
% 30.09/5.70 % (17394)Memory used [KB]: 9338
% 30.09/5.70 % (17394)Time elapsed: 0.447 s
% 30.09/5.70 % (17394)Instructions burned: 908 (million)
% 30.09/5.70 % (17394)------------------------------
% 30.09/5.70 % (17394)------------------------------
% 30.09/5.72 % (17401)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_17169 for (2959ds/5411Mi)
% 30.09/5.78 % (17398)Instruction limit reached!
% 30.09/5.78 % (17398)------------------------------
% 30.09/5.78 % (17398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.09/5.78 % (17398)Termination reason: Unknown
% 30.09/5.78 % (17398)Termination phase: Saturation
% 30.09/5.78
% 30.09/5.78 % (17398)Memory used [KB]: 8315
% 30.09/5.78 % (17398)Time elapsed: 0.214 s
% 30.09/5.78 % (17398)Instructions burned: 444 (million)
% 30.09/5.78 % (17398)------------------------------
% 30.09/5.78 % (17398)------------------------------
% 30.09/5.80 % (17396)Instruction limit reached!
% 30.09/5.80 % (17396)------------------------------
% 30.09/5.80 % (17396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.09/5.80 % (17396)Termination reason: Unknown
% 30.09/5.80 % (17396)Termination phase: Saturation
% 30.09/5.80
% 30.09/5.80 % (17396)Memory used [KB]: 8955
% 30.09/5.80 % (17396)Time elapsed: 0.418 s
% 30.09/5.80 % (17396)Instructions burned: 865 (million)
% 30.09/5.80 % (17396)------------------------------
% 30.09/5.80 % (17396)------------------------------
% 31.00/5.80 % (17402)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_17169 for (2958ds/1762Mi)
% 31.00/5.81 % (17403)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_17169 for (2958ds/96Mi)
% 31.00/5.83 % (17400)Instruction limit reached!
% 31.00/5.83 % (17400)------------------------------
% 31.00/5.83 % (17400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.00/5.83 % (17400)Termination reason: Unknown
% 31.00/5.83 % (17400)Termination phase: Saturation
% 31.00/5.83
% 31.00/5.83 % (17400)Memory used [KB]: 9722
% 31.00/5.83 % (17400)Time elapsed: 0.167 s
% 31.00/5.83 % (17400)Instructions burned: 328 (million)
% 31.00/5.83 % (17400)------------------------------
% 31.00/5.83 % (17400)------------------------------
% 31.00/5.85 % (17404)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_17169 for (2958ds/503Mi)
% 31.00/5.85 % (17403)Instruction limit reached!
% 31.00/5.85 % (17403)------------------------------
% 31.00/5.85 % (17403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.00/5.85 % (17403)Termination reason: Unknown
% 31.00/5.85 % (17403)Termination phase: Property scanning
% 31.00/5.85
% 31.00/5.85 % (17403)Memory used [KB]: 2174
% 31.00/5.85 % (17403)Time elapsed: 0.042 s
% 31.00/5.85 % (17403)Instructions burned: 96 (million)
% 31.00/5.85 % (17403)------------------------------
% 31.00/5.85 % (17403)------------------------------
% 31.00/5.87 % (17405)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_17169 for (2957ds/90Mi)
% 31.00/5.88 % (17399)Instruction limit reached!
% 31.00/5.88 % (17399)------------------------------
% 31.00/5.88 % (17399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.00/5.88 % (17399)Termination reason: Unknown
% 31.00/5.88 % (17399)Termination phase: Saturation
% 31.00/5.88
% 31.00/5.88 % (17399)Memory used [KB]: 8315
% 31.00/5.88 % (17399)Time elapsed: 0.285 s
% 31.00/5.88 % (17399)Instructions burned: 595 (million)
% 31.00/5.88 % (17399)------------------------------
% 31.00/5.88 % (17399)------------------------------
% 31.00/5.90 % (17406)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_17169 for (2957ds/593Mi)
% 32.16/5.91 % (17405)Instruction limit reached!
% 32.16/5.91 % (17405)------------------------------
% 32.16/5.91 % (17405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.16/5.91 % (17405)Termination reason: Unknown
% 32.16/5.91 % (17405)Termination phase: Twee Goal Transformation
% 32.16/5.91
% 32.16/5.91 % (17405)Memory used [KB]: 2558
% 32.16/5.91 % (17405)Time elapsed: 0.040 s
% 32.16/5.91 % (17405)Instructions burned: 90 (million)
% 32.16/5.91 % (17405)------------------------------
% 32.16/5.91 % (17405)------------------------------
% 32.16/5.92 % (17407)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_17169 for (2957ds/1512Mi)
% 33.42/6.09 % (17404)Instruction limit reached!
% 33.42/6.09 % (17404)------------------------------
% 33.42/6.09 % (17404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.42/6.09 % (17404)Termination reason: Unknown
% 33.42/6.09 % (17404)Termination phase: Saturation
% 33.42/6.09
% 33.42/6.09 % (17404)Memory used [KB]: 8315
% 33.42/6.09 % (17404)Time elapsed: 0.245 s
% 33.42/6.09 % (17404)Instructions burned: 504 (million)
% 33.42/6.09 % (17404)------------------------------
% 33.42/6.09 % (17404)------------------------------
% 33.42/6.11 % (17408)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_17169 for (2955ds/569Mi)
% 33.42/6.12 % (17388)Refutation not found, non-redundant clauses discarded% (17388)------------------------------
% 33.42/6.12 % (17388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.42/6.12 % (17388)Termination reason: Refutation not found, non-redundant clauses discarded
% 33.42/6.12
% 33.42/6.12 % (17388)Memory used [KB]: 8187
% 33.42/6.12 % (17388)Time elapsed: 1.824 s
% 33.42/6.12 % (17388)Instructions burned: 4647 (million)
% 33.42/6.12 % (17388)------------------------------
% 33.42/6.12 % (17388)------------------------------
% 33.42/6.14 % (17409)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_17169 for (2955ds/501Mi)
% 34.20/6.16 % (17406)Instruction limit reached!
% 34.20/6.16 % (17406)------------------------------
% 34.20/6.16 % (17406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.20/6.16 % (17406)Termination reason: Unknown
% 34.20/6.16 % (17406)Termination phase: Saturation
% 34.20/6.16
% 34.20/6.16 % (17406)Memory used [KB]: 8443
% 34.20/6.16 % (17406)Time elapsed: 0.290 s
% 34.20/6.16 % (17406)Instructions burned: 594 (million)
% 34.20/6.16 % (17406)------------------------------
% 34.20/6.16 % (17406)------------------------------
% 34.20/6.17 % (17410)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_17169 for (2954ds/562Mi)
% 34.84/6.30 % (17408)Instruction limit reached!
% 34.84/6.30 % (17408)------------------------------
% 34.84/6.30 % (17408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.84/6.30 % (17408)Termination reason: Unknown
% 34.84/6.30 % (17408)Termination phase: Saturation
% 34.84/6.30
% 34.84/6.30 % (17408)Memory used [KB]: 10618
% 34.84/6.30 % (17408)Time elapsed: 0.191 s
% 34.84/6.30 % (17408)Instructions burned: 571 (million)
% 34.84/6.30 % (17408)------------------------------
% 34.84/6.30 % (17408)------------------------------
% 34.84/6.32 % (17411)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_17169 for (2953ds/406Mi)
% 34.84/6.34 % (17409)Instruction limit reached!
% 34.84/6.34 % (17409)------------------------------
% 34.84/6.34 % (17409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.84/6.34 % (17409)Termination reason: Unknown
% 34.84/6.34 % (17409)Termination phase: Saturation
% 34.84/6.34
% 34.84/6.34 % (17409)Memory used [KB]: 9083
% 34.84/6.34 % (17409)Time elapsed: 0.207 s
% 34.84/6.34 % (17409)Instructions burned: 502 (million)
% 34.84/6.34 % (17409)------------------------------
% 34.84/6.34 % (17409)------------------------------
% 34.84/6.35 % (17412)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_17169 for (2952ds/582Mi)
% 34.84/6.37 % (17410)Instruction limit reached!
% 34.84/6.37 % (17410)------------------------------
% 34.84/6.37 % (17410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.84/6.37 % (17410)Termination reason: Unknown
% 34.84/6.37 % (17410)Termination phase: Saturation
% 34.84/6.37
% 34.84/6.37 % (17410)Memory used [KB]: 8315
% 34.84/6.37 % (17410)Time elapsed: 0.201 s
% 34.84/6.37 % (17410)Instructions burned: 563 (million)
% 34.84/6.37 % (17410)------------------------------
% 34.84/6.37 % (17410)------------------------------
% 34.84/6.38 % (17413)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_17169 for (2952ds/456Mi)
% 35.88/6.44 % (17402)Instruction limit reached!
% 35.88/6.44 % (17402)------------------------------
% 35.88/6.44 % (17402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.88/6.44 % (17402)Termination reason: Unknown
% 35.88/6.44 % (17402)Termination phase: Saturation
% 35.88/6.44
% 35.88/6.44 % (17402)Memory used [KB]: 14711
% 35.88/6.44 % (17402)Time elapsed: 0.638 s
% 35.88/6.44 % (17402)Instructions burned: 1763 (million)
% 35.88/6.44 % (17402)------------------------------
% 35.88/6.44 % (17402)------------------------------
% 35.88/6.46 % (17414)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_17169 for (2951ds/393Mi)
% 35.88/6.47 % (17411)Instruction limit reached!
% 35.88/6.47 % (17411)------------------------------
% 35.88/6.47 % (17411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.88/6.47 % (17411)Termination reason: Unknown
% 35.88/6.47 % (17411)Termination phase: Saturation
% 35.88/6.47
% 35.88/6.47 % (17411)Memory used [KB]: 7164
% 35.88/6.47 % (17411)Time elapsed: 0.160 s
% 35.88/6.47 % (17411)Instructions burned: 406 (million)
% 35.88/6.47 % (17411)------------------------------
% 35.88/6.47 % (17411)------------------------------
% 36.39/6.50 % (17415)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_17169 for (2951ds/1335Mi)
% 36.39/6.56 % (17412)Instruction limit reached!
% 36.39/6.56 % (17412)------------------------------
% 36.39/6.56 % (17412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.39/6.56 % (17412)Termination reason: Unknown
% 36.39/6.56 % (17412)Termination phase: Saturation
% 36.39/6.56
% 36.39/6.56 % (17412)Memory used [KB]: 9466
% 36.39/6.56 % (17412)Time elapsed: 0.199 s
% 36.39/6.56 % (17412)Instructions burned: 582 (million)
% 36.39/6.56 % (17412)------------------------------
% 36.39/6.56 % (17412)------------------------------
% 36.39/6.56 % (17413)Instruction limit reached!
% 36.39/6.56 % (17413)------------------------------
% 36.39/6.56 % (17413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.39/6.56 % (17413)Termination reason: Unknown
% 36.39/6.56 % (17413)Termination phase: Saturation
% 36.39/6.56
% 36.39/6.56 % (17413)Memory used [KB]: 8315
% 36.39/6.56 % (17413)Time elapsed: 0.185 s
% 36.39/6.56 % (17413)Instructions burned: 458 (million)
% 36.39/6.56 % (17413)------------------------------
% 36.39/6.56 % (17413)------------------------------
% 36.39/6.57 % (17416)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_17169 for (2950ds/3373Mi)
% 36.39/6.57 % (17407)Instruction limit reached!
% 36.39/6.57 % (17407)------------------------------
% 36.39/6.57 % (17407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.39/6.57 % (17407)Termination reason: Unknown
% 36.39/6.57 % (17407)Termination phase: Saturation
% 36.39/6.57
% 36.39/6.57 % (17407)Memory used [KB]: 10746
% 36.39/6.57 % (17407)Time elapsed: 0.662 s
% 36.39/6.57 % (17407)Instructions burned: 1512 (million)
% 36.39/6.57 % (17407)------------------------------
% 36.39/6.57 % (17407)------------------------------
% 36.39/6.58 % (17417)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_17169 for (2950ds/474Mi)
% 36.39/6.58 % (17418)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_17169 for (2950ds/157Mi)
% 37.06/6.62 % (17418)Instruction limit reached!
% 37.06/6.62 % (17418)------------------------------
% 37.06/6.62 % (17418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.06/6.62 % (17418)Termination reason: Unknown
% 37.06/6.62 % (17418)Termination phase: Saturation
% 37.06/6.62
% 37.06/6.62 % (17418)Memory used [KB]: 6908
% 37.06/6.62 % (17418)Time elapsed: 0.041 s
% 37.06/6.62 % (17418)Instructions burned: 160 (million)
% 37.06/6.62 % (17418)------------------------------
% 37.06/6.62 % (17418)------------------------------
% 37.06/6.63 % (17414)Instruction limit reached!
% 37.06/6.63 % (17414)------------------------------
% 37.06/6.63 % (17414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.06/6.63 % (17414)Termination reason: Unknown
% 37.06/6.63 % (17414)Termination phase: Saturation
% 37.06/6.63
% 37.06/6.63 % (17414)Memory used [KB]: 8443
% 37.06/6.63 % (17414)Time elapsed: 0.188 s
% 37.06/6.63 % (17414)Instructions burned: 394 (million)
% 37.06/6.63 % (17414)------------------------------
% 37.06/6.63 % (17414)------------------------------
% 37.06/6.63 % (17419)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_17169 for (2950ds/590Mi)
% 37.06/6.64 % (17420)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_17169 for (2950ds/104Mi)
% 37.06/6.67 % (17420)Instruction limit reached!
% 37.06/6.67 % (17420)------------------------------
% 37.06/6.67 % (17420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.06/6.67 % (17420)Termination reason: Unknown
% 37.06/6.67 % (17420)Termination phase: Saturation
% 37.06/6.67
% 37.06/6.67 % (17420)Memory used [KB]: 6780
% 37.06/6.67 % (17420)Time elapsed: 0.029 s
% 37.06/6.67 % (17420)Instructions burned: 106 (million)
% 37.06/6.67 % (17420)------------------------------
% 37.06/6.67 % (17420)------------------------------
% 37.06/6.68 % (17421)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_17169 for (2949ds/414Mi)
% 37.52/6.72 % (17417)Instruction limit reached!
% 37.52/6.72 % (17417)------------------------------
% 37.52/6.72 % (17417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.52/6.72 % (17417)Termination reason: Unknown
% 37.52/6.72 % (17417)Termination phase: Saturation
% 37.52/6.72
% 37.52/6.72 % (17417)Memory used [KB]: 10618
% 37.52/6.72 % (17417)Time elapsed: 0.148 s
% 37.52/6.72 % (17417)Instructions burned: 475 (million)
% 37.52/6.72 % (17417)------------------------------
% 37.52/6.72 % (17417)------------------------------
% 37.52/6.73 % (17422)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_17169 for (2949ds/715Mi)
% 37.52/6.78 % (17421)Instruction limit reached!
% 37.52/6.78 % (17421)------------------------------
% 37.52/6.78 % (17421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.52/6.78 % (17421)Termination reason: Unknown
% 37.52/6.78 % (17421)Termination phase: Saturation
% 37.52/6.78
% 37.52/6.78 % (17421)Memory used [KB]: 6908
% 37.52/6.78 % (17421)Time elapsed: 0.107 s
% 37.52/6.78 % (17421)Instructions burned: 415 (million)
% 37.52/6.78 % (17421)------------------------------
% 37.52/6.78 % (17421)------------------------------
% 37.52/6.79 % (17423)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_17169 for (2948ds/961Mi)
% 37.99/6.87 % (17419)Instruction limit reached!
% 37.99/6.87 % (17419)------------------------------
% 37.99/6.87 % (17419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.99/6.87 % (17419)Termination reason: Unknown
% 37.99/6.87 % (17419)Termination phase: Saturation
% 37.99/6.87
% 37.99/6.87 % (17419)Memory used [KB]: 9338
% 37.99/6.87 % (17419)Time elapsed: 0.238 s
% 37.99/6.87 % (17419)Instructions burned: 591 (million)
% 37.99/6.87 % (17419)------------------------------
% 37.99/6.87 % (17419)------------------------------
% 37.99/6.88 % (17424)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_17169 for (2947ds/1213Mi)
% 38.45/6.95 % (17422)Instruction limit reached!
% 38.45/6.95 % (17422)------------------------------
% 38.45/6.95 % (17422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.45/6.95 % (17422)Termination reason: Unknown
% 38.45/6.95 % (17422)Termination phase: Saturation
% 38.45/6.95
% 38.45/6.95 % (17422)Memory used [KB]: 4093
% 38.45/6.95 % (17422)Time elapsed: 0.219 s
% 38.45/6.95 % (17422)Instructions burned: 717 (million)
% 38.45/6.95 % (17422)------------------------------
% 38.45/6.95 % (17422)------------------------------
% 38.45/6.96 % (17425)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_17169 for (2946ds/1979Mi)
% 38.45/6.97 % (17415)Refutation not found, non-redundant clauses discarded% (17415)------------------------------
% 38.45/6.97 % (17415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.45/6.97 % (17415)Termination reason: Refutation not found, non-redundant clauses discarded
% 38.45/6.97
% 38.45/6.97 % (17415)Memory used [KB]: 8827
% 38.45/6.97 % (17415)Time elapsed: 0.474 s
% 38.45/6.97 % (17415)Instructions burned: 1325 (million)
% 38.45/6.97 % (17415)------------------------------
% 38.45/6.97 % (17415)------------------------------
% 38.45/6.98 % (17426)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_17169 for (2946ds/481Mi)
% 40.32/7.09 % (17423)Instruction limit reached!
% 40.32/7.09 % (17423)------------------------------
% 40.32/7.09 % (17423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.32/7.09 % (17423)Termination reason: Unknown
% 40.32/7.09 % (17423)Termination phase: Saturation
% 40.32/7.09
% 40.32/7.09 % (17423)Memory used [KB]: 8699
% 40.32/7.09 % (17423)Time elapsed: 0.296 s
% 40.32/7.09 % (17423)Instructions burned: 962 (million)
% 40.32/7.09 % (17423)------------------------------
% 40.32/7.09 % (17423)------------------------------
% 40.32/7.10 % (17427)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_17169 for (2945ds/783Mi)
% 40.32/7.10 % (17426)Instruction limit reached!
% 40.32/7.10 % (17426)------------------------------
% 40.32/7.10 % (17426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.32/7.10 % (17426)Termination reason: Unknown
% 40.32/7.10 % (17426)Termination phase: Saturation
% 40.32/7.10
% 40.32/7.10 % (17426)Memory used [KB]: 10106
% 40.32/7.10 % (17426)Time elapsed: 0.123 s
% 40.32/7.10 % (17426)Instructions burned: 483 (million)
% 40.32/7.10 % (17426)------------------------------
% 40.32/7.10 % (17426)------------------------------
% 40.32/7.11 % (17428)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_17169 for (2945ds/432Mi)
% 41.38/7.24 % (17428)Instruction limit reached!
% 41.38/7.24 % (17428)------------------------------
% 41.38/7.24 % (17428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.38/7.24 % (17428)Termination reason: Unknown
% 41.38/7.24 % (17428)Termination phase: Saturation
% 41.38/7.24
% 41.38/7.24 % (17428)Memory used [KB]: 8059
% 41.38/7.24 % (17428)Time elapsed: 0.126 s
% 41.38/7.24 % (17428)Instructions burned: 434 (million)
% 41.38/7.24 % (17428)------------------------------
% 41.38/7.24 % (17428)------------------------------
% 41.38/7.25 % (17429)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_17169 for (2944ds/1670Mi)
% 41.38/7.29 % (17424)Instruction limit reached!
% 41.38/7.29 % (17424)------------------------------
% 41.38/7.29 % (17424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.38/7.29 % (17424)Termination reason: Unknown
% 41.38/7.29 % (17424)Termination phase: Saturation
% 41.38/7.29
% 41.38/7.29 % (17424)Memory used [KB]: 12665
% 41.38/7.29 % (17424)Time elapsed: 0.413 s
% 41.38/7.29 % (17424)Instructions burned: 1214 (million)
% 41.38/7.29 % (17424)------------------------------
% 41.38/7.29 % (17424)------------------------------
% 42.02/7.30 % (17430)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_17169 for (2943ds/90Mi)
% 42.02/7.33 % (17430)Instruction limit reached!
% 42.02/7.33 % (17430)------------------------------
% 42.02/7.33 % (17430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.02/7.33 % (17430)Termination reason: Unknown
% 42.02/7.33 % (17430)Termination phase: Saturation
% 42.02/7.33
% 42.02/7.33 % (17430)Memory used [KB]: 2174
% 42.02/7.33 % (17430)Time elapsed: 0.024 s
% 42.02/7.33 % (17430)Instructions burned: 91 (million)
% 42.02/7.33 % (17430)------------------------------
% 42.02/7.33 % (17430)------------------------------
% 42.02/7.34 % (17431)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_17169 for (2943ds/346Mi)
% 42.02/7.34 % (17427)Instruction limit reached!
% 42.02/7.34 % (17427)------------------------------
% 42.02/7.34 % (17427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.02/7.34 % (17427)Termination reason: Unknown
% 42.02/7.34 % (17427)Termination phase: Saturation
% 42.02/7.34
% 42.02/7.34 % (17427)Memory used [KB]: 10362
% 42.02/7.34 % (17427)Time elapsed: 0.242 s
% 42.02/7.34 % (17427)Instructions burned: 783 (million)
% 42.02/7.34 % (17427)------------------------------
% 42.02/7.34 % (17427)------------------------------
% 42.02/7.35 % (17432)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_17169 for (2943ds/401Mi)
% 42.71/7.42 % (17431)Instruction limit reached!
% 42.71/7.42 % (17431)------------------------------
% 42.71/7.42 % (17431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.71/7.42 % (17431)Termination reason: Unknown
% 42.71/7.42 % (17431)Termination phase: Saturation
% 42.71/7.42
% 42.71/7.42 % (17431)Memory used [KB]: 10490
% 42.71/7.42 % (17431)Time elapsed: 0.087 s
% 42.71/7.42 % (17431)Instructions burned: 348 (million)
% 42.71/7.42 % (17431)------------------------------
% 42.71/7.42 % (17431)------------------------------
% 42.71/7.43 % (17433)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_17169 for (2942ds/6454Mi)
% 42.71/7.45 % (17432)Instruction limit reached!
% 42.71/7.45 % (17432)------------------------------
% 42.71/7.45 % (17432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.71/7.45 % (17432)Termination reason: Unknown
% 42.71/7.45 % (17432)Termination phase: Saturation
% 42.71/7.45
% 42.71/7.45 % (17432)Memory used [KB]: 6908
% 42.71/7.45 % (17432)Time elapsed: 0.103 s
% 42.71/7.45 % (17432)Instructions burned: 402 (million)
% 42.71/7.45 % (17432)------------------------------
% 42.71/7.45 % (17432)------------------------------
% 42.71/7.46 % (17434)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_17169 for (2941ds/283Mi)
% 43.31/7.56 % (17434)Instruction limit reached!
% 43.31/7.56 % (17434)------------------------------
% 43.31/7.56 % (17434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.31/7.56 % (17434)Termination reason: Unknown
% 43.31/7.56 % (17434)Termination phase: Saturation
% 43.31/7.56
% 43.31/7.56 % (17434)Memory used [KB]: 7931
% 43.31/7.56 % (17434)Time elapsed: 0.096 s
% 43.31/7.56 % (17434)Instructions burned: 284 (million)
% 43.31/7.56 % (17434)------------------------------
% 43.31/7.56 % (17434)------------------------------
% 43.31/7.57 % (17435)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_17169 for (2940ds/865Mi)
% 43.81/7.61 % (17401)Instruction limit reached!
% 43.81/7.61 % (17401)------------------------------
% 43.81/7.61 % (17401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.81/7.61 % (17401)Termination reason: Unknown
% 43.81/7.61 % (17401)Termination phase: Saturation
% 43.81/7.61
% 43.81/7.61 % (17401)Memory used [KB]: 14200
% 43.81/7.61 % (17401)Time elapsed: 1.910 s
% 43.81/7.61 % (17401)Instructions burned: 5413 (million)
% 43.81/7.61 % (17401)------------------------------
% 43.81/7.61 % (17401)------------------------------
% 43.81/7.62 % (17436)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_17169 for (2940ds/4528Mi)
% 43.81/7.62 % (17425)Instruction limit reached!
% 43.81/7.62 % (17425)------------------------------
% 43.81/7.62 % (17425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.81/7.62 % (17425)Termination reason: Unknown
% 43.81/7.62 % (17425)Termination phase: Saturation
% 43.81/7.62
% 43.81/7.62 % (17425)Memory used [KB]: 9210
% 43.81/7.62 % (17425)Time elapsed: 0.660 s
% 43.81/7.62 % (17425)Instructions burned: 1980 (million)
% 43.81/7.62 % (17425)------------------------------
% 43.81/7.62 % (17425)------------------------------
% 43.81/7.63 % (17437)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_17169 for (2940ds/1001Mi)
% 43.81/7.66 % (17429)Instruction limit reached!
% 43.81/7.66 % (17429)------------------------------
% 43.81/7.66 % (17429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.81/7.66 % (17429)Termination reason: Unknown
% 43.81/7.66 % (17429)Termination phase: Saturation
% 43.81/7.66
% 43.81/7.66 % (17429)Memory used [KB]: 11769
% 43.81/7.66 % (17429)Time elapsed: 0.411 s
% 43.81/7.66 % (17429)Instructions burned: 1670 (million)
% 43.81/7.66 % (17429)------------------------------
% 43.81/7.66 % (17429)------------------------------
% 43.81/7.66 % (17416)Instruction limit reached!
% 43.81/7.66 % (17416)------------------------------
% 43.81/7.66 % (17416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.81/7.66 % (17416)Termination reason: Unknown
% 43.81/7.66 % (17416)Termination phase: Saturation
% 43.81/7.66
% 43.81/7.66 % (17416)Memory used [KB]: 11641
% 43.81/7.66 % (17416)Time elapsed: 1.089 s
% 43.81/7.66 % (17416)Instructions burned: 3373 (million)
% 43.81/7.66 % (17416)------------------------------
% 43.81/7.66 % (17416)------------------------------
% 43.81/7.67 % (17438)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_17169 for (2939ds/102Mi)
% 43.81/7.67 % (17439)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_17169 for (2939ds/952Mi)
% 44.46/7.70 % (17438)Instruction limit reached!
% 44.46/7.70 % (17438)------------------------------
% 44.46/7.70 % (17438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.46/7.70 % (17438)Termination reason: Unknown
% 44.46/7.70 % (17438)Termination phase: Saturation
% 44.46/7.70
% 44.46/7.70 % (17438)Memory used [KB]: 6780
% 44.46/7.70 % (17438)Time elapsed: 0.030 s
% 44.46/7.70 % (17438)Instructions burned: 103 (million)
% 44.46/7.70 % (17438)------------------------------
% 44.46/7.70 % (17438)------------------------------
% 44.46/7.71 % (17440)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_17169 for (2939ds/578Mi)
% 44.46/7.72 % (17436)Refutation not found, incomplete strategy
% 44.46/7.72 % (17436)------------------------------
% 44.46/7.72 % (17436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.46/7.72 % (17436)Termination reason: Refutation not found, incomplete strategy
% 44.46/7.72
% 44.46/7.72
% 44.46/7.72 % (17436)Memory used [KB]: 2430
% 44.46/7.72 % (17436)Time elapsed: 0.098 s
% 44.46/7.72 % (17436)Instructions burned: 341 (million)
% 44.46/7.72 % (17436)------------------------------
% 44.46/7.72 % (17436)------------------------------
% 44.46/7.73 % (17441)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_17169 for (2939ds/643Mi)
% 44.71/7.82 % (17435)Instruction limit reached!
% 44.71/7.82 % (17435)------------------------------
% 44.71/7.82 % (17435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.71/7.82 % (17435)Termination reason: Unknown
% 44.71/7.82 % (17435)Termination phase: Saturation
% 44.71/7.82
% 44.71/7.82 % (17435)Memory used [KB]: 8187
% 44.71/7.82 % (17435)Time elapsed: 0.256 s
% 44.71/7.82 % (17435)Instructions burned: 866 (million)
% 44.71/7.82 % (17435)------------------------------
% 44.71/7.82 % (17435)------------------------------
% 44.71/7.83 % (17442)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_17169 for (2938ds/865Mi)
% 44.71/7.84 % (17440)Instruction limit reached!
% 44.71/7.84 % (17440)------------------------------
% 44.71/7.84 % (17440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.71/7.84 % (17440)Termination reason: Unknown
% 44.71/7.84 % (17440)Termination phase: Saturation
% 44.71/7.84
% 44.71/7.84 % (17440)Memory used [KB]: 8443
% 44.71/7.84 % (17440)Time elapsed: 0.130 s
% 44.71/7.84 % (17440)Instructions burned: 579 (million)
% 44.71/7.84 % (17440)------------------------------
% 44.71/7.84 % (17440)------------------------------
% 44.71/7.85 % (17443)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_17169 for (2938ds/1174Mi)
% 44.71/7.88 % (17389)Instruction limit reached!
% 44.71/7.88 % (17389)------------------------------
% 44.71/7.88 % (17389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.71/7.88 % (17389)Termination reason: Unknown
% 44.71/7.88 % (17389)Termination phase: Saturation
% 44.71/7.88
% 44.71/7.88 % (17389)Memory used [KB]: 23666
% 44.71/7.88 % (17389)Time elapsed: 3.563 s
% 44.71/7.88 % (17389)Instructions burned: 8251 (million)
% 44.71/7.88 % (17389)------------------------------
% 44.71/7.88 % (17389)------------------------------
% 44.71/7.89 % (17444)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_17169 for (2937ds/644Mi)
% 44.71/7.89 % (17441)Instruction limit reached!
% 44.71/7.89 % (17441)------------------------------
% 44.71/7.89 % (17441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.71/7.89 % (17441)Termination reason: Unknown
% 44.71/7.89 % (17441)Termination phase: Saturation
% 44.71/7.89
% 44.71/7.89 % (17441)Memory used [KB]: 10490
% 44.71/7.89 % (17441)Time elapsed: 0.168 s
% 44.71/7.89 % (17441)Instructions burned: 645 (million)
% 44.71/7.89 % (17441)------------------------------
% 44.71/7.89 % (17441)------------------------------
% 45.39/7.90 % (17445)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_17169 for (2937ds/1201Mi)
% 45.39/7.95 % (17437)Instruction limit reached!
% 45.39/7.95 % (17437)------------------------------
% 45.39/7.95 % (17437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.39/7.95 % (17437)Termination reason: Unknown
% 45.39/7.95 % (17437)Termination phase: Saturation
% 45.39/7.95
% 45.39/7.95 % (17437)Memory used [KB]: 10234
% 45.39/7.95 % (17437)Time elapsed: 0.324 s
% 45.39/7.95 % (17437)Instructions burned: 1002 (million)
% 45.39/7.95 % (17437)------------------------------
% 45.39/7.95 % (17437)------------------------------
% 45.39/7.96 % (17446)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_17169 for (2936ds/1046Mi)
% 45.39/8.02 % (17439)Instruction limit reached!
% 45.39/8.02 % (17439)------------------------------
% 45.39/8.02 % (17439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.39/8.02 % (17439)Termination reason: Unknown
% 45.39/8.02 % (17439)Termination phase: Saturation
% 45.39/8.02
% 45.39/8.02 % (17439)Memory used [KB]: 8699
% 45.39/8.02 % (17439)Time elapsed: 0.371 s
% 45.39/8.02 % (17439)Instructions burned: 954 (million)
% 45.39/8.02 % (17439)------------------------------
% 45.39/8.02 % (17439)------------------------------
% 47.31/8.03 % (17447)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_17169 for (2936ds/222Mi)
% 47.31/8.08 % (17442)Instruction limit reached!
% 47.31/8.08 % (17442)------------------------------
% 47.31/8.08 % (17442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.31/8.08 % (17442)Termination reason: Unknown
% 47.31/8.08 % (17442)Termination phase: Saturation
% 47.31/8.08
% 47.31/8.08 % (17442)Memory used [KB]: 7291
% 47.31/8.08 % (17442)Time elapsed: 0.268 s
% 47.31/8.08 % (17442)Instructions burned: 866 (million)
% 47.31/8.08 % (17442)------------------------------
% 47.31/8.08 % (17442)------------------------------
% 47.31/8.09 % (17447)Instruction limit reached!
% 47.31/8.09 % (17447)------------------------------
% 47.31/8.09 % (17447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.31/8.09 % (17447)Termination reason: Unknown
% 47.31/8.09 % (17447)Termination phase: Saturation
% 47.31/8.09
% 47.31/8.09 % (17447)Memory used [KB]: 6780
% 47.31/8.09 % (17447)Time elapsed: 0.058 s
% 47.31/8.09 % (17447)Instructions burned: 222 (million)
% 47.31/8.09 % (17447)------------------------------
% 47.31/8.09 % (17447)------------------------------
% 47.31/8.09 % (17448)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_17169 for (2935ds/68Mi)
% 47.31/8.10 % (17444)Instruction limit reached!
% 47.31/8.10 % (17444)------------------------------
% 47.31/8.10 % (17444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.31/8.10 % (17444)Termination reason: Unknown
% 47.31/8.10 % (17444)Termination phase: Saturation
% 47.31/8.10
% 47.31/8.10 % (17444)Memory used [KB]: 7675
% 47.31/8.10 % (17444)Time elapsed: 0.208 s
% 47.31/8.10 % (17444)Instructions burned: 646 (million)
% 47.31/8.10 % (17444)------------------------------
% 47.31/8.10 % (17444)------------------------------
% 47.31/8.10 % (17449)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_17169 for (2935ds/454Mi)
% 47.31/8.11 % (17448)Instruction limit reached!
% 47.31/8.11 % (17448)------------------------------
% 47.31/8.11 % (17448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.31/8.11 % (17448)Termination reason: Unknown
% 47.31/8.11 % (17448)Termination phase: Property scanning
% 47.31/8.11
% 47.31/8.11 % (17448)Memory used [KB]: 2046
% 47.31/8.11 % (17448)Time elapsed: 0.018 s
% 47.31/8.11 % (17448)Instructions burned: 68 (million)
% 47.31/8.11 % (17448)------------------------------
% 47.31/8.11 % (17448)------------------------------
% 47.31/8.11 % (17450)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_17169 for (2935ds/360Mi)
% 47.31/8.12 % (17451)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_17169 for (2935ds/157Mi)
% 47.98/8.16 % (17451)Instruction limit reached!
% 47.98/8.16 % (17451)------------------------------
% 47.98/8.16 % (17451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.98/8.16 % (17451)Termination reason: Unknown
% 47.98/8.16 % (17451)Termination phase: Saturation
% 47.98/8.16
% 47.98/8.16 % (17451)Memory used [KB]: 6780
% 47.98/8.16 % (17451)Time elapsed: 0.041 s
% 47.98/8.16 % (17451)Instructions burned: 160 (million)
% 47.98/8.16 % (17451)------------------------------
% 47.98/8.16 % (17451)------------------------------
% 47.98/8.17 % (17452)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_17169 for (2934ds/5061Mi)
% 47.98/8.19 % (17450)Instruction limit reached!
% 47.98/8.19 % (17450)------------------------------
% 47.98/8.19 % (17450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.98/8.19 % (17450)Termination reason: Unknown
% 47.98/8.19 % (17450)Termination phase: Saturation
% 47.98/8.19
% 47.98/8.19 % (17450)Memory used [KB]: 6908
% 47.98/8.19 % (17450)Time elapsed: 0.088 s
% 47.98/8.19 % (17450)Instructions burned: 360 (million)
% 47.98/8.19 % (17450)------------------------------
% 47.98/8.19 % (17450)------------------------------
% 48.41/8.20 % (17453)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_17169 for (2934ds/2401Mi)
% 48.41/8.21 % (17449)Instruction limit reached!
% 48.41/8.21 % (17449)------------------------------
% 48.41/8.21 % (17449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.41/8.21 % (17449)Termination reason: Unknown
% 48.41/8.21 % (17449)Termination phase: Saturation
% 48.41/8.21
% 48.41/8.21 % (17449)Memory used [KB]: 15351
% 48.41/8.21 % (17449)Time elapsed: 0.117 s
% 48.41/8.21 % (17449)Instructions burned: 457 (million)
% 48.41/8.21 % (17449)------------------------------
% 48.41/8.21 % (17449)------------------------------
% 48.41/8.22 % (17454)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_17169 for (2934ds/5798Mi)
% 48.41/8.22 % (17446)Instruction limit reached!
% 48.41/8.22 % (17446)------------------------------
% 48.41/8.22 % (17446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.41/8.22 % (17446)Termination reason: Unknown
% 48.41/8.22 % (17446)Termination phase: Saturation
% 48.41/8.22
% 48.41/8.22 % (17446)Memory used [KB]: 6908
% 48.41/8.22 % (17446)Time elapsed: 0.258 s
% 48.41/8.22 % (17446)Instructions burned: 1047 (million)
% 48.41/8.22 % (17446)------------------------------
% 48.41/8.22 % (17446)------------------------------
% 48.41/8.22 % (17443)Instruction limit reached!
% 48.41/8.22 % (17443)------------------------------
% 48.41/8.22 % (17443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.41/8.22 % (17443)Termination reason: Unknown
% 48.41/8.22 % (17443)Termination phase: Saturation
% 48.41/8.22
% 48.41/8.22 % (17443)Memory used [KB]: 8827
% 48.41/8.22 % (17443)Time elapsed: 0.397 s
% 48.41/8.22 % (17443)Instructions burned: 1175 (million)
% 48.41/8.22 % (17443)------------------------------
% 48.41/8.22 % (17443)------------------------------
% 48.41/8.23 % (17455)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_17169 for (2934ds/346Mi)
% 48.41/8.23 % (17456)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_17169 for (2934ds/1321Mi)
% 48.41/8.24 % (17445)Instruction limit reached!
% 48.41/8.24 % (17445)------------------------------
% 48.41/8.24 % (17445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.41/8.24 % (17445)Termination reason: Unknown
% 48.41/8.24 % (17445)Termination phase: Saturation
% 48.41/8.24
% 48.41/8.24 % (17445)Memory used [KB]: 9722
% 48.41/8.24 % (17445)Time elapsed: 0.362 s
% 48.41/8.24 % (17445)Instructions burned: 1201 (million)
% 48.41/8.24 % (17445)------------------------------
% 48.41/8.24 % (17445)------------------------------
% 48.41/8.25 % (17457)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_17169 for (2933ds/1312Mi)
% 48.76/8.32 % (17455)Instruction limit reached!
% 48.76/8.32 % (17455)------------------------------
% 48.76/8.32 % (17455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.76/8.32 % (17455)Termination reason: Unknown
% 48.76/8.32 % (17455)Termination phase: Saturation
% 48.76/8.32
% 48.76/8.32 % (17455)Memory used [KB]: 9850
% 48.76/8.32 % (17455)Time elapsed: 0.087 s
% 48.76/8.32 % (17455)Instructions burned: 349 (million)
% 48.76/8.32 % (17455)------------------------------
% 48.76/8.32 % (17455)------------------------------
% 48.76/8.33 % (17458)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_17169 for (2933ds/672Mi)
% 49.07/8.54 % (17458)Instruction limit reached!
% 49.07/8.54 % (17458)------------------------------
% 49.07/8.54 % (17458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.07/8.54 % (17458)Termination reason: Unknown
% 49.07/8.54 % (17458)Termination phase: Saturation
% 49.07/8.54
% 49.07/8.54 % (17458)Memory used [KB]: 9594
% 49.07/8.54 % (17458)Time elapsed: 0.207 s
% 49.07/8.54 % (17458)Instructions burned: 674 (million)
% 49.07/8.54 % (17458)------------------------------
% 49.07/8.54 % (17458)------------------------------
% 49.07/8.55 % (17459)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_17169 for (2931ds/1897Mi)
% 49.07/8.59 % (17457)Instruction limit reached!
% 49.07/8.59 % (17457)------------------------------
% 49.07/8.59 % (17457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.07/8.59 % (17457)Termination reason: Unknown
% 49.07/8.59 % (17457)Termination phase: Saturation
% 49.07/8.59
% 49.07/8.59 % (17457)Memory used [KB]: 11385
% 49.07/8.59 % (17457)Time elapsed: 0.334 s
% 49.07/8.59 % (17457)Instructions burned: 1312 (million)
% 49.07/8.59 % (17457)------------------------------
% 49.07/8.59 % (17457)------------------------------
% 49.71/8.60 % (17460)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_17169 for (2930ds/1202Mi)
% 49.71/8.62 % (17456)Instruction limit reached!
% 49.71/8.62 % (17456)------------------------------
% 49.71/8.62 % (17456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.71/8.62 % (17456)Termination reason: Unknown
% 49.71/8.62 % (17456)Termination phase: Saturation
% 49.71/8.62
% 49.71/8.62 % (17456)Memory used [KB]: 6652
% 49.71/8.62 % (17456)Time elapsed: 0.383 s
% 49.71/8.62 % (17456)Instructions burned: 1323 (million)
% 49.71/8.62 % (17456)------------------------------
% 49.71/8.62 % (17456)------------------------------
% 49.71/8.63 % (17461)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_17169 for (2930ds/1493Mi)
% 50.41/8.93 % (17453)Instruction limit reached!
% 50.41/8.93 % (17453)------------------------------
% 50.41/8.93 % (17453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.41/8.93 % (17453)Termination reason: Unknown
% 50.41/8.93 % (17453)Termination phase: Saturation
% 50.41/8.93
% 50.41/8.93 % (17453)Memory used [KB]: 8827
% 50.41/8.93 % (17453)Time elapsed: 0.724 s
% 50.41/8.93 % (17453)Instructions burned: 2402 (million)
% 50.41/8.93 % (17453)------------------------------
% 50.41/8.93 % (17453)------------------------------
% 50.41/8.94 % (17462)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_17169 for (2927ds/7679Mi)
% 50.41/8.94 % (17460)Instruction limit reached!
% 50.41/8.94 % (17460)------------------------------
% 50.41/8.94 % (17460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.41/8.94 % (17460)Termination reason: Unknown
% 50.41/8.94 % (17460)Termination phase: Saturation
% 50.41/8.94
% 50.41/8.94 % (17460)Memory used [KB]: 6652
% 50.41/8.94 % (17460)Time elapsed: 0.346 s
% 50.41/8.94 % (17460)Instructions burned: 1203 (million)
% 50.41/8.94 % (17460)------------------------------
% 50.41/8.94 % (17460)------------------------------
% 50.41/8.95 % (17463)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_17169 for (2926ds/340Mi)
% 50.41/8.98 % (17461)Instruction limit reached!
% 50.41/8.98 % (17461)------------------------------
% 50.41/8.98 % (17461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.41/8.98 % (17461)Termination reason: Unknown
% 50.41/8.98 % (17461)Termination phase: Saturation
% 50.41/8.98
% 50.41/8.98 % (17461)Memory used [KB]: 7164
% 50.41/8.98 % (17461)Time elapsed: 0.354 s
% 50.41/8.98 % (17461)Instructions burned: 1495 (million)
% 50.41/8.98 % (17461)------------------------------
% 50.41/8.98 % (17461)------------------------------
% 50.41/8.99 % (17464)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_17169 for (2926ds/3672Mi)
% 54.30/9.05 % (17463)Instruction limit reached!
% 54.30/9.05 % (17463)------------------------------
% 54.30/9.05 % (17463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.30/9.05 % (17463)Termination reason: Unknown
% 54.30/9.05 % (17463)Termination phase: Saturation
% 54.30/9.05
% 54.30/9.05 % (17463)Memory used [KB]: 9210
% 54.30/9.05 % (17463)Time elapsed: 0.103 s
% 54.30/9.05 % (17463)Instructions burned: 340 (million)
% 54.30/9.05 % (17463)------------------------------
% 54.30/9.05 % (17463)------------------------------
% 54.30/9.06 % (17465)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_17169 for (2925ds/1535Mi)
% 54.95/9.13 % (17459)Instruction limit reached!
% 54.95/9.13 % (17459)------------------------------
% 54.95/9.13 % (17459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.95/9.13 % (17459)Termination reason: Unknown
% 54.95/9.13 % (17459)Termination phase: Saturation
% 54.95/9.13
% 54.95/9.13 % (17459)Memory used [KB]: 12025
% 54.95/9.13 % (17459)Time elapsed: 0.585 s
% 54.95/9.13 % (17459)Instructions burned: 1898 (million)
% 54.95/9.13 % (17459)------------------------------
% 54.95/9.13 % (17459)------------------------------
% 54.95/9.14 % (17466)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_17169 for (2925ds/4637Mi)
% 56.30/9.44 % (17465)Instruction limit reached!
% 56.30/9.44 % (17465)------------------------------
% 56.30/9.44 % (17465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.30/9.44 % (17465)Termination reason: Unknown
% 56.30/9.44 % (17465)Termination phase: Saturation
% 56.30/9.44
% 56.30/9.44 % (17465)Memory used [KB]: 11129
% 56.30/9.44 % (17465)Time elapsed: 0.377 s
% 56.30/9.44 % (17465)Instructions burned: 1538 (million)
% 56.30/9.44 % (17465)------------------------------
% 56.30/9.44 % (17465)------------------------------
% 56.30/9.44 % (17433)Instruction limit reached!
% 56.30/9.44 % (17433)------------------------------
% 56.30/9.44 % (17433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.30/9.44 % (17433)Termination reason: Unknown
% 56.30/9.44 % (17433)Termination phase: Saturation
% 56.30/9.44
% 56.30/9.44 % (17433)Memory used [KB]: 11897
% 56.30/9.44 % (17433)Time elapsed: 2.012 s
% 56.30/9.44 % (17433)Instructions burned: 6456 (million)
% 56.30/9.44 % (17433)------------------------------
% 56.30/9.44 % (17433)------------------------------
% 56.30/9.45 % (17467)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_17169 for (2922ds/3174Mi)
% 56.30/9.45 % (17468)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_17169 for (2922ds/307Mi)
% 56.30/9.46 % (17452)Instruction limit reached!
% 56.30/9.46 % (17452)------------------------------
% 56.30/9.46 % (17452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.30/9.46 % (17452)Termination reason: Unknown
% 56.30/9.46 % (17452)Termination phase: Saturation
% 56.30/9.46
% 56.30/9.46 % (17452)Memory used [KB]: 9594
% 56.30/9.46 % (17452)Time elapsed: 1.295 s
% 56.30/9.46 % (17452)Instructions burned: 5063 (million)
% 56.30/9.46 % (17452)------------------------------
% 56.30/9.46 % (17452)------------------------------
% 56.30/9.47 % (17469)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_17169 for (2921ds/3619Mi)
% 57.13/9.53 % (17468)Instruction limit reached!
% 57.13/9.53 % (17468)------------------------------
% 57.13/9.53 % (17468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.13/9.53 % (17468)Termination reason: Unknown
% 57.13/9.53 % (17468)Termination phase: Saturation
% 57.13/9.53
% 57.13/9.53 % (17468)Memory used [KB]: 6908
% 57.13/9.53 % (17468)Time elapsed: 0.077 s
% 57.13/9.53 % (17468)Instructions burned: 310 (million)
% 57.13/9.53 % (17468)------------------------------
% 57.13/9.53 % (17468)------------------------------
% 57.13/9.54 % (17470)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_17169 for (2921ds/2325Mi)
% 58.11/9.84 % (17470)Refutation not found, non-redundant clauses discarded% (17470)------------------------------
% 58.11/9.84 % (17470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.11/9.84 % (17470)Termination reason: Refutation not found, non-redundant clauses discarded
% 58.11/9.84
% 58.11/9.84 % (17470)Memory used [KB]: 12281
% 58.11/9.84 % (17470)Time elapsed: 0.305 s
% 58.11/9.84 % (17470)Instructions burned: 1031 (million)
% 58.11/9.84 % (17470)------------------------------
% 58.11/9.84 % (17470)------------------------------
% 58.11/9.86 % (17471)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_17169 for (2918ds/2341Mi)
% 58.73/9.99 % (17454)Instruction limit reached!
% 58.73/9.99 % (17454)------------------------------
% 58.73/9.99 % (17454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.73/9.99 % (17454)Termination reason: Unknown
% 58.73/9.99 % (17454)Termination phase: Saturation
% 58.73/9.99
% 58.73/9.99 % (17454)Memory used [KB]: 13304
% 58.73/9.99 % (17454)Time elapsed: 1.767 s
% 58.73/9.99 % (17454)Instructions burned: 5798 (million)
% 58.73/9.99 % (17454)------------------------------
% 58.73/9.99 % (17454)------------------------------
% 58.73/10.00 % (17472)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_17169 for (2916ds/7257Mi)
% 61.97/10.14 % (17464)Instruction limit reached!
% 61.97/10.14 % (17464)------------------------------
% 61.97/10.14 % (17464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.97/10.14 % (17464)Termination reason: Unknown
% 61.97/10.14 % (17464)Termination phase: Saturation
% 61.97/10.14
% 61.97/10.14 % (17464)Memory used [KB]: 12025
% 61.97/10.14 % (17464)Time elapsed: 1.161 s
% 61.97/10.14 % (17464)Instructions burned: 3673 (million)
% 61.97/10.14 % (17464)------------------------------
% 61.97/10.14 % (17464)------------------------------
% 61.97/10.15 % (17473)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_17169 for (2915ds/3710Mi)
% 63.64/10.40 % (17467)Instruction limit reached!
% 63.64/10.40 % (17467)------------------------------
% 63.64/10.40 % (17467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.64/10.40 % (17467)Termination reason: Unknown
% 63.64/10.40 % (17467)Termination phase: Saturation
% 63.64/10.40
% 63.64/10.40 % (17467)Memory used [KB]: 17142
% 63.64/10.40 % (17467)Time elapsed: 0.972 s
% 63.64/10.40 % (17467)Instructions burned: 3177 (million)
% 63.64/10.40 % (17467)------------------------------
% 63.64/10.40 % (17467)------------------------------
% 63.64/10.41 % (17474)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_17169 for (2912ds/326Mi)
% 64.16/10.51 % (17474)Instruction limit reached!
% 64.16/10.51 % (17474)------------------------------
% 64.16/10.51 % (17474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.16/10.51 % (17474)Termination reason: Unknown
% 64.16/10.51 % (17474)Termination phase: Saturation
% 64.16/10.51
% 64.16/10.51 % (17474)Memory used [KB]: 7931
% 64.16/10.51 % (17474)Time elapsed: 0.095 s
% 64.16/10.51 % (17474)Instructions burned: 327 (million)
% 64.16/10.51 % (17474)------------------------------
% 64.16/10.51 % (17474)------------------------------
% 64.16/10.51 % (17469)Instruction limit reached!
% 64.16/10.51 % (17469)------------------------------
% 64.16/10.51 % (17469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.16/10.51 % (17469)Termination reason: Unknown
% 64.16/10.51 % (17469)Termination phase: Saturation
% 64.16/10.51
% 64.16/10.51 % (17469)Memory used [KB]: 11641
% 64.16/10.51 % (17469)Time elapsed: 1.052 s
% 64.16/10.51 % (17469)Instructions burned: 3622 (million)
% 64.16/10.51 % (17469)------------------------------
% 64.16/10.51 % (17469)------------------------------
% 64.16/10.52 % (17475)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_17169 for (2911ds/1100Mi)
% 64.16/10.52 % (17476)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_17169 for (2911ds/406Mi)
% 64.16/10.56 % (17466)Instruction limit reached!
% 64.16/10.56 % (17466)------------------------------
% 64.16/10.56 % (17466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.16/10.56 % (17466)Termination reason: Unknown
% 64.16/10.56 % (17466)Termination phase: Saturation
% 64.16/10.56
% 64.16/10.56 % (17466)Memory used [KB]: 10362
% 64.16/10.56 % (17466)Time elapsed: 1.441 s
% 64.16/10.56 % (17466)Instructions burned: 4639 (million)
% 64.16/10.56 % (17466)------------------------------
% 64.16/10.56 % (17466)------------------------------
% 64.16/10.57 % (17471)Instruction limit reached!
% 64.16/10.57 % (17471)------------------------------
% 64.16/10.57 % (17471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.16/10.57 % (17471)Termination reason: Unknown
% 64.16/10.57 % (17471)Termination phase: Saturation
% 64.16/10.57
% 64.16/10.57 % (17471)Memory used [KB]: 9850
% 64.16/10.57 % (17471)Time elapsed: 0.714 s
% 64.16/10.57 % (17471)Instructions burned: 2342 (million)
% 64.16/10.57 % (17471)------------------------------
% 64.16/10.57 % (17471)------------------------------
% 64.16/10.57 % (17477)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_17169 for (2910ds/1871Mi)
% 64.16/10.58 % (17478)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_17169 for (2910ds/1194Mi)
% 64.63/10.63 % (17476)Instruction limit reached!
% 64.63/10.63 % (17476)------------------------------
% 64.63/10.63 % (17476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.63/10.63 % (17476)Termination reason: Unknown
% 64.63/10.63 % (17476)Termination phase: Saturation
% 64.63/10.63
% 64.63/10.63 % (17476)Memory used [KB]: 7164
% 64.63/10.63 % (17476)Time elapsed: 0.112 s
% 64.63/10.63 % (17476)Instructions burned: 406 (million)
% 64.63/10.63 % (17476)------------------------------
% 64.63/10.63 % (17476)------------------------------
% 64.63/10.64 % (17479)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_17169 for (2909ds/474Mi)
% 64.96/10.76 % (17479)Instruction limit reached!
% 64.96/10.76 % (17479)------------------------------
% 64.96/10.76 % (17479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.96/10.76 % (17479)Termination reason: Unknown
% 64.96/10.76 % (17479)Termination phase: Saturation
% 64.96/10.76
% 64.96/10.76 % (17479)Memory used [KB]: 10106
% 64.96/10.76 % (17479)Time elapsed: 0.121 s
% 64.96/10.76 % (17479)Instructions burned: 476 (million)
% 64.96/10.76 % (17479)------------------------------
% 64.96/10.76 % (17479)------------------------------
% 64.96/10.77 % (17480)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_17169 for (2908ds/3115Mi)
% 65.29/10.86 % (17475)Instruction limit reached!
% 65.29/10.86 % (17475)------------------------------
% 65.29/10.86 % (17475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.29/10.86 % (17475)Termination reason: Unknown
% 65.29/10.86 % (17475)Termination phase: Saturation
% 65.29/10.86
% 65.29/10.86 % (17475)Memory used [KB]: 12153
% 65.29/10.86 % (17475)Time elapsed: 0.343 s
% 65.29/10.86 % (17475)Instructions burned: 1102 (million)
% 65.29/10.86 % (17475)------------------------------
% 65.29/10.86 % (17475)------------------------------
% 65.29/10.87 % (17481)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_17169 for (2907ds/831Mi)
% 65.84/10.95 % (17478)Instruction limit reached!
% 65.84/10.95 % (17478)------------------------------
% 65.84/10.95 % (17478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.84/10.95 % (17478)Termination reason: Unknown
% 65.84/10.95 % (17478)Termination phase: Saturation
% 65.84/10.95
% 65.84/10.95 % (17478)Memory used [KB]: 10874
% 65.84/10.95 % (17478)Time elapsed: 0.372 s
% 65.84/10.95 % (17478)Instructions burned: 1197 (million)
% 65.84/10.95 % (17478)------------------------------
% 65.84/10.95 % (17478)------------------------------
% 65.84/10.96 % (17482)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_17169 for (2906ds/1188Mi)
% 68.24/11.07 % (17473)Instruction limit reached!
% 68.24/11.07 % (17473)------------------------------
% 68.24/11.07 % (17473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.24/11.07 % (17473)Termination reason: Unknown
% 68.24/11.07 % (17473)Termination phase: Saturation
% 68.24/11.07
% 68.24/11.07 % (17473)Memory used [KB]: 12409
% 68.24/11.08 % (17473)Time elapsed: 0.922 s
% 68.24/11.08 % (17473)Instructions burned: 3713 (million)
% 68.24/11.08 % (17473)------------------------------
% 68.24/11.08 % (17473)------------------------------
% 68.24/11.09 % (17483)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_17169 for (2905ds/2868Mi)
% 68.92/11.13 % (17481)Instruction limit reached!
% 68.92/11.13 % (17481)------------------------------
% 68.92/11.13 % (17481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.92/11.13 % (17481)Termination reason: Unknown
% 68.92/11.13 % (17481)Termination phase: Saturation
% 68.92/11.13
% 68.92/11.13 % (17481)Memory used [KB]: 8571
% 68.92/11.13 % (17481)Time elapsed: 0.258 s
% 68.92/11.13 % (17481)Instructions burned: 832 (million)
% 68.92/11.13 % (17481)------------------------------
% 68.92/11.13 % (17481)------------------------------
% 68.92/11.14 % (17484)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_17169 for (2905ds/1516Mi)
% 68.92/11.14 % (17477)Instruction limit reached!
% 68.92/11.14 % (17477)------------------------------
% 68.92/11.14 % (17477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.92/11.14 % (17477)Termination reason: Unknown
% 68.92/11.14 % (17477)Termination phase: Saturation
% 68.92/11.14
% 68.92/11.14 % (17477)Memory used [KB]: 15863
% 68.92/11.14 % (17477)Time elapsed: 0.569 s
% 68.92/11.14 % (17477)Instructions burned: 1874 (million)
% 68.92/11.14 % (17477)------------------------------
% 68.92/11.14 % (17477)------------------------------
% 68.92/11.15 % (17485)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_17169 for (2904ds/2321Mi)
% 68.92/11.19 % (17462)Instruction limit reached!
% 68.92/11.19 % (17462)------------------------------
% 68.92/11.19 % (17462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.92/11.19 % (17462)Termination reason: Unknown
% 68.92/11.19 % (17462)Termination phase: Saturation
% 68.92/11.19
% 68.92/11.19 % (17462)Memory used [KB]: 17270
% 68.92/11.19 % (17462)Time elapsed: 2.251 s
% 68.92/11.19 % (17462)Instructions burned: 7681 (million)
% 68.92/11.19 % (17462)------------------------------
% 68.92/11.19 % (17462)------------------------------
% 69.23/11.20 % (17486)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_17169 for (2904ds/2812Mi)
% 69.23/11.26 % (17482)Instruction limit reached!
% 69.23/11.26 % (17482)------------------------------
% 69.23/11.26 % (17482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.23/11.26 % (17482)Termination reason: Unknown
% 69.23/11.26 % (17482)Termination phase: Saturation
% 69.23/11.26
% 69.23/11.26 % (17482)Memory used [KB]: 11897
% 69.23/11.26 % (17482)Time elapsed: 0.298 s
% 69.23/11.26 % (17482)Instructions burned: 1191 (million)
% 69.23/11.26 % (17482)------------------------------
% 69.23/11.26 % (17482)------------------------------
% 69.23/11.27 % (17487)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_17169 for (2903ds/4604Mi)
% 69.90/11.54 % (17480)Instruction limit reached!
% 69.90/11.54 % (17480)------------------------------
% 69.90/11.54 % (17480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.90/11.54 % (17480)Termination reason: Unknown
% 69.90/11.54 % (17480)Termination phase: Saturation
% 69.90/11.54
% 69.90/11.54 % (17480)Memory used [KB]: 11129
% 69.90/11.54 % (17480)Time elapsed: 0.778 s
% 69.90/11.54 % (17480)Instructions burned: 3117 (million)
% 69.90/11.54 % (17480)------------------------------
% 69.90/11.54 % (17480)------------------------------
% 69.90/11.55 % (17488)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_17169 for (2900ds/2678Mi)
% 69.90/11.59 % (17484)Instruction limit reached!
% 69.90/11.59 % (17484)------------------------------
% 69.90/11.59 % (17484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.90/11.59 % (17484)Termination reason: Unknown
% 69.90/11.59 % (17484)Termination phase: Saturation
% 69.90/11.59
% 69.90/11.59 % (17484)Memory used [KB]: 11385
% 69.90/11.59 % (17484)Time elapsed: 0.453 s
% 69.90/11.59 % (17484)Instructions burned: 1519 (million)
% 69.90/11.59 % (17484)------------------------------
% 69.90/11.59 % (17484)------------------------------
% 70.51/11.60 % (17489)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_17169 for (2900ds/643Mi)
% 70.61/11.73 % (17485)Instruction limit reached!
% 70.61/11.73 % (17485)------------------------------
% 70.61/11.73 % (17485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.61/11.73 % (17485)Termination reason: Unknown
% 70.61/11.73 % (17485)Termination phase: Saturation
% 70.61/11.73
% 70.61/11.73 % (17485)Memory used [KB]: 11129
% 70.61/11.73 % (17485)Time elapsed: 0.579 s
% 70.61/11.73 % (17485)Instructions burned: 2323 (million)
% 70.61/11.73 % (17485)------------------------------
% 70.61/11.73 % (17485)------------------------------
% 70.61/11.74 % (17490)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_17169 for (2899ds/458Mi)
% 70.61/11.76 % (17489)Instruction limit reached!
% 70.61/11.76 % (17489)------------------------------
% 70.61/11.76 % (17489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.61/11.76 % (17489)Termination reason: Unknown
% 70.61/11.76 % (17489)Termination phase: Saturation
% 70.61/11.76
% 70.61/11.76 % (17489)Memory used [KB]: 10106
% 70.61/11.76 % (17489)Time elapsed: 0.161 s
% 70.61/11.76 % (17489)Instructions burned: 644 (million)
% 70.61/11.76 % (17489)------------------------------
% 70.61/11.76 % (17489)------------------------------
% 70.61/11.77 % (17491)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_17169 for (2898ds/2546Mi)
% 70.61/11.77 % (17483)Instruction limit reached!
% 70.61/11.77 % (17483)------------------------------
% 70.61/11.77 % (17483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.61/11.77 % (17483)Termination reason: Unknown
% 70.61/11.77 % (17483)Termination phase: Saturation
% 70.61/11.77
% 70.61/11.77 % (17483)Memory used [KB]: 6908
% 70.61/11.77 % (17483)Time elapsed: 0.687 s
% 70.61/11.77 % (17483)Instructions burned: 2869 (million)
% 70.61/11.77 % (17483)------------------------------
% 70.61/11.77 % (17483)------------------------------
% 70.61/11.78 % (17492)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_17169 for (2898ds/1432Mi)
% 72.17/11.85 % (17490)Instruction limit reached!
% 72.17/11.85 % (17490)------------------------------
% 72.17/11.85 % (17490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.17/11.85 % (17490)Termination reason: Unknown
% 72.17/11.85 % (17490)Termination phase: Saturation
% 72.17/11.85
% 72.17/11.85 % (17490)Memory used [KB]: 10618
% 72.17/11.85 % (17490)Time elapsed: 0.115 s
% 72.17/11.85 % (17490)Instructions burned: 460 (million)
% 72.17/11.85 % (17490)------------------------------
% 72.17/11.85 % (17490)------------------------------
% 72.17/11.86 % (17493)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_17169 for (2897ds/386Mi)
% 72.40/11.96 % (17493)Instruction limit reached!
% 72.40/11.96 % (17493)------------------------------
% 72.40/11.96 % (17493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.40/11.96 % (17493)Termination reason: Unknown
% 72.40/11.96 % (17493)Termination phase: Saturation
% 72.40/11.96
% 72.40/11.96 % (17493)Memory used [KB]: 6908
% 72.40/11.96 % (17493)Time elapsed: 0.096 s
% 72.40/11.96 % (17493)Instructions burned: 390 (million)
% 72.40/11.96 % (17493)------------------------------
% 72.40/11.96 % (17493)------------------------------
% 72.40/11.97 % (17494)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_17169 for (2896ds/360Mi)
% 75.18/12.06 % (17486)Instruction limit reached!
% 75.18/12.06 % (17486)------------------------------
% 75.18/12.06 % (17486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.18/12.06 % (17486)Termination reason: Unknown
% 75.18/12.06 % (17486)Termination phase: Saturation
% 75.18/12.06
% 75.18/12.06 % (17486)Memory used [KB]: 10746
% 75.18/12.06 % (17486)Time elapsed: 0.866 s
% 75.18/12.06 % (17486)Instructions burned: 2813 (million)
% 75.18/12.06 % (17486)------------------------------
% 75.18/12.06 % (17486)------------------------------
% 75.18/12.06 % (17494)Instruction limit reached!
% 75.18/12.06 % (17494)------------------------------
% 75.18/12.06 % (17494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.18/12.06 % (17494)Termination reason: Unknown
% 75.18/12.06 % (17494)Termination phase: Saturation
% 75.18/12.06
% 75.18/12.06 % (17494)Memory used [KB]: 6908
% 75.18/12.06 % (17494)Time elapsed: 0.097 s
% 75.18/12.06 % (17494)Instructions burned: 363 (million)
% 75.18/12.06 % (17494)------------------------------
% 75.18/12.06 % (17494)------------------------------
% 75.18/12.07 % (17495)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_17169 for (2895ds/5446Mi)
% 75.18/12.07 % (17496)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_17169 for (2895ds/2573Mi)
% 75.78/12.13 % (17492)Instruction limit reached!
% 75.78/12.13 % (17492)------------------------------
% 75.78/12.13 % (17492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.78/12.13 % (17492)Termination reason: Unknown
% 75.78/12.13 % (17492)Termination phase: Saturation
% 75.78/12.13
% 75.78/12.13 % (17492)Memory used [KB]: 14583
% 75.78/12.13 % (17492)Time elapsed: 0.344 s
% 75.78/12.13 % (17492)Instructions burned: 1435 (million)
% 75.78/12.13 % (17492)------------------------------
% 75.78/12.13 % (17492)------------------------------
% 75.78/12.14 % (17497)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_17169 for (2895ds/2655Mi)
% 75.78/12.18 % (17472)Instruction limit reached!
% 75.78/12.18 % (17472)------------------------------
% 75.78/12.18 % (17472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.78/12.18 % (17472)Termination reason: Unknown
% 75.78/12.18 % (17472)Termination phase: Saturation
% 75.78/12.18
% 75.78/12.18 % (17472)Memory used [KB]: 10362
% 75.78/12.18 % (17472)Time elapsed: 2.205 s
% 75.78/12.18 % (17472)Instructions burned: 7259 (million)
% 75.78/12.18 % (17472)------------------------------
% 75.78/12.18 % (17472)------------------------------
% 75.78/12.19 % (17498)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_17169 for (2894ds/2781Mi)
% 76.10/12.21 % (17488)Instruction limit reached!
% 76.10/12.21 % (17488)------------------------------
% 76.10/12.21 % (17488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.10/12.21 % (17488)Termination reason: Unknown
% 76.10/12.21 % (17488)Termination phase: Saturation
% 76.10/12.21
% 76.10/12.21 % (17488)Memory used [KB]: 15095
% 76.10/12.21 % (17488)Time elapsed: 0.661 s
% 76.10/12.21 % (17488)Instructions burned: 2680 (million)
% 76.10/12.21 % (17488)------------------------------
% 76.10/12.21 % (17488)------------------------------
% 76.10/12.23 % (17499)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_17169 for (2894ds/307Mi)
% 76.33/12.30 % (17499)Instruction limit reached!
% 76.33/12.30 % (17499)------------------------------
% 76.33/12.30 % (17499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.33/12.30 % (17499)Termination reason: Unknown
% 76.33/12.30 % (17499)Termination phase: Saturation
% 76.33/12.30
% 76.33/12.30 % (17499)Memory used [KB]: 6908
% 76.33/12.30 % (17499)Time elapsed: 0.077 s
% 76.33/12.30 % (17499)Instructions burned: 307 (million)
% 76.33/12.30 % (17499)------------------------------
% 76.33/12.30 % (17499)------------------------------
% 76.33/12.31 % (17500)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_17169 for (2893ds/1548Mi)
% 76.61/12.45 % (17491)First to succeed.
% 76.61/12.46 % (17491)Refutation found. Thanks to Tanya!
% 76.61/12.46 % SZS status Theorem for DTF2THF_17169
% 76.61/12.46 % SZS output start Proof for DTF2THF_17169
% 76.61/12.46 thf(func_def_0, type, in: $i > $i > $o).
% 76.61/12.46 thf(func_def_1, type, exu: ($i > $o) > $o).
% 76.61/12.46 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 76.61/12.46 thf(func_def_8, type, powerset: $i > $i).
% 76.61/12.46 thf(func_def_10, type, setunion: $i > $i).
% 76.61/12.46 thf(func_def_19, type, descr: ($i > $o) > $i).
% 76.61/12.46 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 76.61/12.46 thf(func_def_26, type, prop2set: $o > $i).
% 76.61/12.46 thf(func_def_36, type, nonempty: $i > $o).
% 76.61/12.46 thf(func_def_69, type, set2prop: $i > $o).
% 76.61/12.46 thf(func_def_88, type, subset: $i > $i > $o).
% 76.61/12.46 thf(func_def_89, type, disjoint: $i > $i > $o).
% 76.61/12.46 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 76.61/12.46 thf(func_def_114, type, binunion: $i > $i > $i).
% 76.61/12.46 thf(func_def_122, type, binintersect: $i > $i > $i).
% 76.61/12.46 thf(func_def_135, type, regular: $i > $o).
% 76.61/12.46 thf(func_def_136, type, setminus: $i > $i > $i).
% 76.61/12.46 thf(func_def_147, type, symdiff: $i > $i > $i).
% 76.61/12.46 thf(func_def_153, type, iskpair: $i > $o).
% 76.61/12.46 thf(func_def_158, type, kpair: $i > $i > $i).
% 76.61/12.46 thf(func_def_160, type, cartprod: $i > $i > $i).
% 76.61/12.46 thf(func_def_177, type, singleton: $i > $o).
% 76.61/12.46 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 76.61/12.46 thf(func_def_184, type, atmost1p: $i > $o).
% 76.61/12.46 thf(func_def_185, type, atleast2p: $i > $o).
% 76.61/12.46 thf(func_def_186, type, atmost2p: $i > $o).
% 76.61/12.46 thf(func_def_187, type, upairsetp: $i > $o).
% 76.61/12.46 thf(func_def_191, type, kfst: $i > $i).
% 76.61/12.46 thf(func_def_203, type, ksnd: $i > $i).
% 76.61/12.46 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 76.61/12.46 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 76.61/12.46 thf(func_def_222, type, func: $i > $i > $i > $o).
% 76.61/12.46 thf(func_def_223, type, funcSet: $i > $i > $i).
% 76.61/12.46 thf(func_def_242, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 76.61/12.46 thf(func_def_243, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 76.61/12.46 thf(func_def_249, type, ph7: !>[X0: $tType]:(X0)).
% 76.61/12.46 thf(f8478,plain,(
% 76.61/12.46 $false),
% 76.61/12.46 inference(avatar_sat_refutation,[status(thm)],[f1531,f1536,f1654,f1668,f3763,f3785,f3802,f3841,f3870,f4186,f8447,f8453,f8470])).
% 76.61/12.46 thf(f8470,plain,(
% 76.61/12.46 ~spl6_229),
% 76.61/12.46 inference(avatar_contradiction_clause,[status(thm)],[f8469])).
% 76.61/12.46 thf(f8469,plain,(
% 76.61/12.46 $false | ~spl6_229),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f8468])).
% 76.61/12.46 thf(f8468,plain,(
% 76.61/12.46 ($true = $false) | ~spl6_229),
% 76.61/12.46 inference(duplicate_literal_removal,[status(thm)],[f8461])).
% 76.61/12.46 thf(f8461,plain,(
% 76.61/12.46 ($true = $false) | ($true = $false) | ~spl6_229),
% 76.61/12.46 inference(superposition,[status(thm)],[f599,f8452])).
% 76.61/12.46 thf(f8452,plain,(
% 76.61/12.46 (($true & $false) = $true) | ~spl6_229),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f8450])).
% 76.61/12.46 thf(f8450,definition,(
% 76.61/12.46 spl6_229 <=> (($true & $false) = $true)),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_229])],[avatar_definition])).
% 76.61/12.46 thf(f599,plain,(
% 76.61/12.46 ( ! [X2 : $o,X1 : $o] : (((X1 & X2) = $false) | ($true = X2)) )),
% 76.61/12.46 introduced(definition,[],[logical_and_proxy_axiom])).
% 76.61/12.46 thf(f8453,plain,(
% 76.61/12.46 spl6_229 | ~spl6_90),
% 76.61/12.46 inference(avatar_split_clause,[status(thm)],[f8448,f4183,f8450])).
% 76.61/12.46 thf(f4183,definition,(
% 76.61/12.46 spl6_90 <=> ($true = ((subset @ sK3 @ (cartprod @ sK2 @ sK4)) & $false))),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_90])],[avatar_definition])).
% 76.61/12.46 thf(f8448,plain,(
% 76.61/12.46 (($true & $false) = $true) | ~spl6_90),
% 76.61/12.46 inference(forward_demodulation,[status(thm)],[f4185,f4175])).
% 76.61/12.46 thf(f4175,plain,(
% 76.61/12.46 ($true = (subset @ sK3 @ (cartprod @ sK2 @ sK4)))),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f4168])).
% 76.61/12.46 thf(f4168,plain,(
% 76.61/12.46 ($true = (subset @ sK3 @ (cartprod @ sK2 @ sK4))) | ($true = $false)),
% 76.61/12.46 inference(superposition,[status(thm)],[f1215,f598])).
% 76.61/12.46 thf(f598,plain,(
% 76.61/12.46 ( ! [X2 : $o,X1 : $o] : (((X1 & X2) = $false) | ($true = X1)) )),
% 76.61/12.46 introduced(definition,[],[logical_and_proxy_axiom])).
% 76.61/12.46 thf(f1215,plain,(
% 76.61/12.46 (((subset @ sK3 @ (cartprod @ sK2 @ sK4)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK3)))) & (in @ Y1 @ (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK3))))))))))) = $true)),
% 76.61/12.46 inference(beta_eta_normalization,[status(thm)],[f1072])).
% 76.61/12.46 thf(f1072,plain,(
% 76.61/12.46 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))) @ sK2 @ sK4 @ sK3))),
% 76.61/12.46 inference(definition_unfolding,[status(thm)],[f757,f1004])).
% 76.61/12.46 thf(f1004,plain,(
% 76.61/12.46 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 76.61/12.46 inference(definition_unfolding,[status(thm)],[f636,f901,f1002])).
% 76.61/12.46 thf(f1002,plain,(
% 76.61/12.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 76.61/12.46 inference(definition_unfolding,[status(thm)],[f653,f894])).
% 76.61/12.46 thf(f894,plain,(
% 76.61/12.46 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f243])).
% 76.61/12.46 thf(f243,plain,(
% 76.61/12.46 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 76.61/12.46 inference(fool_elimination,[status(thm)],[f242])).
% 76.61/12.46 thf(f242,plain,(
% 76.61/12.46 (singleton = (^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))))),
% 76.61/12.46 inference(rectify,[status(thm)],[f156])).
% 76.61/12.46 thf(f156,axiom,(
% 76.61/12.46 (singleton = (^[X3 : $i] : (? [X1 : $i] : ((in @ X1 @ X3) & ((setadjoin @ X1 @ emptyset) = X3)))))),
% 76.61/12.46 file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',singleton)).
% 76.61/12.46 thf(f653,plain,(
% 76.61/12.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f353])).
% 76.61/12.46 thf(f353,plain,(
% 76.61/12.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 76.61/12.46 inference(fool_elimination,[status(thm)],[f352])).
% 76.61/12.46 thf(f352,plain,(
% 76.61/12.46 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 76.61/12.46 inference(rectify,[status(thm)],[f158])).
% 76.61/12.46 thf(f158,axiom,(
% 76.61/12.46 ((^[X3 : $i, X0 : $i > $o] : (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))))) = ex1)),
% 76.61/12.46 file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',ex1)).
% 76.61/12.46 thf(f901,plain,(
% 76.61/12.46 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f233])).
% 76.61/12.46 thf(f233,plain,(
% 76.61/12.46 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 76.61/12.46 inference(fool_elimination,[status(thm)],[f232])).
% 76.61/12.46 thf(f232,plain,(
% 76.61/12.46 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 76.61/12.46 inference(rectify,[status(thm)],[f186])).
% 76.61/12.46 thf(f186,axiom,(
% 76.61/12.46 (breln = (^[X3 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X3 @ X4))))),
% 76.61/12.46 file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',breln)).
% 76.61/12.46 thf(f636,plain,(
% 76.61/12.46 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f425])).
% 76.61/12.46 thf(f425,plain,(
% 76.61/12.46 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 76.61/12.46 inference(fool_elimination,[status(thm)],[f424])).
% 76.61/12.46 thf(f424,plain,(
% 76.61/12.46 ((^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))) = func)),
% 76.61/12.46 inference(rectify,[status(thm)],[f194])).
% 76.61/12.46 thf(f194,axiom,(
% 76.61/12.46 ((^[X3 : $i, X4 : $i, X12 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (ex1 @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X12)))) & (breln @ X3 @ X4 @ X12))) = func)),
% 76.61/12.46 file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',func)).
% 76.61/12.46 thf(f757,plain,(
% 76.61/12.46 ($true = (func @ sK2 @ sK4 @ sK3))),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f608])).
% 76.61/12.46 thf(f608,plain,(
% 76.61/12.46 (disjointsetsI1 = $true) & (symdiffIneg1 = $true) & (quantDeMorgan4 = $true) & (setminusERneg = $true) & (dpsetconstrI = $true) & (dsetconstr__Cong = $true) & (cartprodmempair = $true) & (binintersectI = $true) & (setukpairinjL1 = $true) & (emptyI = $true) & (foundationAx = $true) & (eqimpsubset1 = $true) & (setoftrueEq = $true) & (setminusSubset1 = $true) & (emptysetsubset = $true) & (setadjoinSub2 = $true) & (subset2powerset = $true) & (setadjoinSub = $true) & (exuE2 = $true) & (emptyinPowerset = $true) & (setukpairIL = $true) & (setminusILneg = $true) & (setadjoinIR = $true) & (binintersectSubset4 = $true) & (setminusEL = $true) & (eqinunit = $true) & (kpairsurjEq = $true) & (noeltsimpempty = $true) & (subsetE2 = $true) & (dpsetconstrSub = $true) & (descr__Cong = $true) & (sepSubset = $true) & (upairequniteq = $true) & (setunionE = $true) & (cartprodfstpairEq = $true) & (dpsetconstrEL2 = $true) & (kpairiskpair = $true) & (singletonsubset = $true) & (exuE1 = $true) & (setadjoinAx = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (powersetAx = $true) & (subsetE = $true) & (ubforcartprodlem1 = $true) & (cartprodmempair1 = $true) & (eqimpsubset2 = $true) & (upairsetIR = $true) & (setunionE2 = $true) & (cartprodsndpairEq = $true) & (theprop = $true) & (binintersectSubset1 = $true) & (powersetI = $true) & (setminusER = $true) & (dpsetconstrEL1 = $true) & (exuE3u = $true) & (powersetsubset = $true) & (emptyset__Cong = $true) & (sepInPowerset = $true) & (setukpairinjR12 = $true) & (setminusSubset2 = $true) & (upairinpowunion = $true) & (setukpairinjR11 = $true) & (binunionE = $true) & (emptysetAx = $true) & (quantDeMorgan3 = $true) & (prop2set2propI = $true) & (exuI1 = $true) & (ex1I2 = $true) & (upairsetIL = $true) & (cartprodpairsurjEq = $true) & (emptyInPowerset = $true) & (setunion__Cong = $true) & (vacuousDall = $true) & (subsetRefl = $true) & (omegaSAx = $true) & (setukpairIR = $true) & (cartprodmempaircEq = $true) & (dpsetconstrER = $true) & (ubforcartprodlem3 = $true) & (emptyE1 = $true) & (ex1I = $true) & (dpsetconstrERa = $true) & (setunionsingleton2 = $true) & (descrp = $true) & (binintersectLsub = $true) & (quantDeMorgan2 = $true) & (setOfPairsIsBReln = $true) & (symdiffI2 = $true) & (binunionEcases = $true) & (notdexE = $true) & (secondinupair = $true) & (ksndpairEq = $true) & (ubforcartprodlem2 = $true) & (kfstsingleton = $true) & (bs114d = $true) & (cartprodfstin = $true) & (setadjoinIL = $true) & (setukpairinjR2 = $true) & (notdallE = $true) & (notinsingleton = $true) & (binintersectSubset2 = $true) & (upairset2IR = $true) & (setminusLsub = $true) & (setextAx = $true) & (emptysetE = $true) & (setadjoinE = $true) & (binunionRsub = $true) & (subPowSU = $true) & (setunionAx = $true) & (nonemptyImpWitness = $true) & (binunionLsub = $true) & (cartprodpairmemEL = $true) & (emptysetimpfalse = $true) & (wellorderingAx = $true) & (exuI2 = $true) & (subsetemptysetimpeq = $true) & (powersetE1 = $true) & (setextsub = $true) & (setukpairinjL = $true) & (setadjoin__Cong = $true) & (notequalI2 = $true) & (binintersectSubset3 = $true) & (binunionIL = $true) & (nonemptyI = $true) & (setminusELneg = $true) & (upairset2E = $true) & (powersetE = $true) & (binintersectER = $true) & (ex1E1 = $true) & (prop2setI = $true) & (exuEu = $true) & (upairsubunion = $true) & (exuE3e = $true) & (($true = (func @ sK2 @ sK4 @ sK3)) & (($true != (singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (in @ (kpair @ sK5 @ Y0) @ sK3))))) & ((in @ sK5 @ sK2) = $true))) & (subsetTrans = $true) & (nonemptyI1 = $true) & (powerset__Cong = $true) & (setunionI = $true) & (kfstpairEq = $true) & (singletoninpowerset = $true) & (setadjoinOr = $true) & (emptyinunitempty = $true) & (notsubsetI = $true) & (upairsetE = $true) & (in__Cong = $true) & (uniqinunit = $true) & (subsetI1 = $true) & (binintersectEL = $true) & (omega0Ax = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (inCongP = $true) & (exuI3 = $true) & (symdiffI1 = $true) & (singletonprop = $true) & (notinemptyset = $true) & (quantDeMorgan1 = $true) & (symdiffE = $true) & (setukpairinjR1 = $true) & (notequalI1 = $true) & (setukpairinjR = $true) & (kpairp = $true) & (omegaIndAx = $true) & (inPowerset = $true) & (replAx = $true) & (cartprodpairin = $true) & (exu__Cong = $true) & (prop2setE = $true) & (binintersectRsub = $true) & (binintersectSubset5 = $true) & (setukpairinjL2 = $true) & (ksndsingleton = $true) & (setminusIRneg = $true) & (singletoninpowunion = $true) & (binunionIR = $true) & (singletonsswitch = $true) & (singletonsuniq = $true) & (symdiffIneg2 = $true) & (setunionsingleton = $true) & (cartprodsndin = $true) & (setext = $true) & (omega__Cong = $true) & (dsetconstrI = $true) & (powersetI1 = $true) & (cartprodpairmemER = $true) & (setminusI = $true) & (subsetI2 = $true) & (setunionsingleton1 = $true)),
% 76.61/12.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f605,f607,f606])).
% 76.61/12.46 thf(f606,plain,(
% 76.61/12.46 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) & ? [X3 : $i] : (($true != (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) & ($true = (in @ X3 @ X0)))) => (($true = (func @ sK2 @ sK4 @ sK3)) & ? [X3 : $i] : (($true != (singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ sK3))))) & ($true = (in @ X3 @ sK2))))),
% 76.61/12.46 introduced(definition,[],[choice_axiom])).
% 76.61/12.46 thf(f607,plain,(
% 76.61/12.46 ? [X3 : $i] : (($true != (singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ sK3))))) & ($true = (in @ X3 @ sK2))) => (($true != (singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (in @ (kpair @ sK5 @ Y0) @ sK3))))) & ((in @ sK5 @ sK2) = $true))),
% 76.61/12.46 introduced(definition,[],[choice_axiom])).
% 76.61/12.46 thf(f605,plain,(
% 76.61/12.46 (disjointsetsI1 = $true) & (symdiffIneg1 = $true) & (quantDeMorgan4 = $true) & (setminusERneg = $true) & (dpsetconstrI = $true) & (dsetconstr__Cong = $true) & (cartprodmempair = $true) & (binintersectI = $true) & (setukpairinjL1 = $true) & (emptyI = $true) & (foundationAx = $true) & (eqimpsubset1 = $true) & (setoftrueEq = $true) & (setminusSubset1 = $true) & (emptysetsubset = $true) & (setadjoinSub2 = $true) & (subset2powerset = $true) & (setadjoinSub = $true) & (exuE2 = $true) & (emptyinPowerset = $true) & (setukpairIL = $true) & (setminusILneg = $true) & (setadjoinIR = $true) & (binintersectSubset4 = $true) & (setminusEL = $true) & (eqinunit = $true) & (kpairsurjEq = $true) & (noeltsimpempty = $true) & (subsetE2 = $true) & (dpsetconstrSub = $true) & (descr__Cong = $true) & (sepSubset = $true) & (upairequniteq = $true) & (setunionE = $true) & (cartprodfstpairEq = $true) & (dpsetconstrEL2 = $true) & (kpairiskpair = $true) & (singletonsubset = $true) & (exuE1 = $true) & (setadjoinAx = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (powersetAx = $true) & (subsetE = $true) & (ubforcartprodlem1 = $true) & (cartprodmempair1 = $true) & (eqimpsubset2 = $true) & (upairsetIR = $true) & (setunionE2 = $true) & (cartprodsndpairEq = $true) & (theprop = $true) & (binintersectSubset1 = $true) & (powersetI = $true) & (setminusER = $true) & (dpsetconstrEL1 = $true) & (exuE3u = $true) & (powersetsubset = $true) & (emptyset__Cong = $true) & (sepInPowerset = $true) & (setukpairinjR12 = $true) & (setminusSubset2 = $true) & (upairinpowunion = $true) & (setukpairinjR11 = $true) & (binunionE = $true) & (emptysetAx = $true) & (quantDeMorgan3 = $true) & (prop2set2propI = $true) & (exuI1 = $true) & (ex1I2 = $true) & (upairsetIL = $true) & (cartprodpairsurjEq = $true) & (emptyInPowerset = $true) & (setunion__Cong = $true) & (vacuousDall = $true) & (subsetRefl = $true) & (omegaSAx = $true) & (setukpairIR = $true) & (cartprodmempaircEq = $true) & (dpsetconstrER = $true) & (ubforcartprodlem3 = $true) & (emptyE1 = $true) & (ex1I = $true) & (dpsetconstrERa = $true) & (setunionsingleton2 = $true) & (descrp = $true) & (binintersectLsub = $true) & (quantDeMorgan2 = $true) & (setOfPairsIsBReln = $true) & (symdiffI2 = $true) & (binunionEcases = $true) & (notdexE = $true) & (secondinupair = $true) & (ksndpairEq = $true) & (ubforcartprodlem2 = $true) & (kfstsingleton = $true) & (bs114d = $true) & (cartprodfstin = $true) & (setadjoinIL = $true) & (setukpairinjR2 = $true) & (notdallE = $true) & (notinsingleton = $true) & (binintersectSubset2 = $true) & (upairset2IR = $true) & (setminusLsub = $true) & (setextAx = $true) & (emptysetE = $true) & (setadjoinE = $true) & (binunionRsub = $true) & (subPowSU = $true) & (setunionAx = $true) & (nonemptyImpWitness = $true) & (binunionLsub = $true) & (cartprodpairmemEL = $true) & (emptysetimpfalse = $true) & (wellorderingAx = $true) & (exuI2 = $true) & (subsetemptysetimpeq = $true) & (powersetE1 = $true) & (setextsub = $true) & (setukpairinjL = $true) & (setadjoin__Cong = $true) & (notequalI2 = $true) & (binintersectSubset3 = $true) & (binunionIL = $true) & (nonemptyI = $true) & (setminusELneg = $true) & (upairset2E = $true) & (powersetE = $true) & (binintersectER = $true) & (ex1E1 = $true) & (prop2setI = $true) & (exuEu = $true) & (upairsubunion = $true) & (exuE3e = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) & ? [X3 : $i] : (($true != (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) & ($true = (in @ X3 @ X0)))) & (subsetTrans = $true) & (nonemptyI1 = $true) & (powerset__Cong = $true) & (setunionI = $true) & (kfstpairEq = $true) & (singletoninpowerset = $true) & (setadjoinOr = $true) & (emptyinunitempty = $true) & (notsubsetI = $true) & (upairsetE = $true) & (in__Cong = $true) & (uniqinunit = $true) & (subsetI1 = $true) & (binintersectEL = $true) & (omega0Ax = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (inCongP = $true) & (exuI3 = $true) & (symdiffI1 = $true) & (singletonprop = $true) & (notinemptyset = $true) & (quantDeMorgan1 = $true) & (symdiffE = $true) & (setukpairinjR1 = $true) & (notequalI1 = $true) & (setukpairinjR = $true) & (kpairp = $true) & (omegaIndAx = $true) & (inPowerset = $true) & (replAx = $true) & (cartprodpairin = $true) & (exu__Cong = $true) & (prop2setE = $true) & (binintersectRsub = $true) & (binintersectSubset5 = $true) & (setukpairinjL2 = $true) & (ksndsingleton = $true) & (setminusIRneg = $true) & (singletoninpowunion = $true) & (binunionIR = $true) & (singletonsswitch = $true) & (singletonsuniq = $true) & (symdiffIneg2 = $true) & (setunionsingleton = $true) & (cartprodsndin = $true) & (setext = $true) & (omega__Cong = $true) & (dsetconstrI = $true) & (powersetI1 = $true) & (cartprodpairmemER = $true) & (setminusI = $true) & (subsetI2 = $true) & (setunionsingleton1 = $true)),
% 76.61/12.46 inference(flattening,[status(thm)],[f604])).
% 76.61/12.46 thf(f604,plain,(
% 76.61/12.46 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) & ? [X3 : $i] : (($true != (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) & ($true = (in @ X3 @ X0)))) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 76.61/12.46 inference(ennf_transformation,[status(thm)],[f249])).
% 76.61/12.46 thf(f249,plain,(
% 76.61/12.46 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => ($true = (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 76.61/12.46 inference(fool_elimination,[status(thm)],[f248])).
% 76.61/12.46 thf(f248,plain,(
% 76.61/12.46 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X2 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 76.61/12.46 inference(rectify,[status(thm)],[f197])).
% 76.61/12.46 thf(f197,negated_conjecture,(
% 76.61/12.46 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => ! [X3 : $i,X13 : $i,X4 : $i] : ((func @ X3 @ X4 @ X13) => ! [X1 : $i] : ((in @ X1 @ X3) => (singleton @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 76.61/12.46 inference(negated_conjecture,[status(cth)],[f196])).
% 76.61/12.46 thf(f196,conjecture,(
% 76.61/12.46 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => ! [X3 : $i,X13 : $i,X4 : $i] : ((func @ X3 @ X4 @ X13) => ! [X1 : $i] : ((in @ X1 @ X3) => (singleton @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 76.61/12.46 file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',funcImageSingleton)).
% 76.61/12.46 thf(f4185,plain,(
% 76.61/12.46 ($true = ((subset @ sK3 @ (cartprod @ sK2 @ sK4)) & $false)) | ~spl6_90),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f4183])).
% 76.61/12.46 thf(f8447,plain,(
% 76.61/12.46 ~spl6_87 | ~spl6_89),
% 76.61/12.46 inference(avatar_contradiction_clause,[status(thm)],[f8446])).
% 76.61/12.46 thf(f8446,plain,(
% 76.61/12.46 $false | (~spl6_87 | ~spl6_89)),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f8445])).
% 76.61/12.46 thf(f8445,plain,(
% 76.61/12.46 ($true = $false) | (~spl6_87 | ~spl6_89)),
% 76.61/12.46 inference(forward_demodulation,[status(thm)],[f8444,f3869])).
% 76.61/12.46 thf(f3869,plain,(
% 76.61/12.46 ($false = ($true => $false)) | ~spl6_87),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f3867])).
% 76.61/12.46 thf(f3867,definition,(
% 76.61/12.46 spl6_87 <=> ($false = ($true => $false))),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_87])],[avatar_definition])).
% 76.61/12.46 thf(f8444,plain,(
% 76.61/12.46 ($true = ($true => $false)) | ~spl6_89),
% 76.61/12.46 inference(forward_demodulation,[status(thm)],[f8414,f755])).
% 76.61/12.46 thf(f755,plain,(
% 76.61/12.46 ((in @ sK5 @ sK2) = $true)),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f608])).
% 76.61/12.46 thf(f8414,plain,(
% 76.61/12.46 (((in @ sK5 @ sK2) => $false) = $true) | ~spl6_89),
% 76.61/12.46 inference(superposition,[status(thm)],[f4181,f3726])).
% 76.61/12.46 thf(f3726,plain,(
% 76.61/12.46 ($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK3)))) & (in @ Y0 @ (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK3))))))))),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f3722])).
% 76.61/12.46 thf(f3722,plain,(
% 76.61/12.46 ($true != $true) | ($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK3)))) & (in @ Y0 @ (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK3))))))))),
% 76.61/12.46 inference(fool_paramodulation,[status(thm)],[f1197])).
% 76.61/12.46 thf(f1197,plain,(
% 76.61/12.46 ($true != (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK3)))) & (in @ Y0 @ (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK3))))))))),
% 76.61/12.46 inference(beta_eta_normalization,[status(thm)],[f1073])).
% 76.61/12.46 thf(f1073,plain,(
% 76.61/12.46 ($true != ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))) @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (in @ (kpair @ sK5 @ Y0) @ sK3)))))),
% 76.61/12.46 inference(definition_unfolding,[status(thm)],[f756,f894])).
% 76.61/12.46 thf(f756,plain,(
% 76.61/12.46 ($true != (singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (in @ (kpair @ sK5 @ Y0) @ sK3)))))),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f608])).
% 76.61/12.46 thf(f4181,plain,(
% 76.61/12.46 ( ! [X0 : $i] : ((((in @ X0 @ sK2) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ X0 @ Y1) @ sK3)))) & (in @ Y0 @ (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ X0 @ Y1) @ sK3)))))))) = $true)) ) | ~spl6_89),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f4180])).
% 76.61/12.46 thf(f4180,definition,(
% 76.61/12.46 spl6_89 <=> ! [X0 : $i] : (((in @ X0 @ sK2) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ X0 @ Y1) @ sK3)))) & (in @ Y0 @ (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ X0 @ Y1) @ sK3)))))))) = $true)),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_89])],[avatar_definition])).
% 76.61/12.46 thf(f4186,plain,(
% 76.61/12.46 spl6_89 | spl6_90),
% 76.61/12.46 inference(avatar_split_clause,[status(thm)],[f4178,f4183,f4180])).
% 76.61/12.46 thf(f4178,plain,(
% 76.61/12.46 ( ! [X0 : $i] : ((((in @ X0 @ sK2) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ X0 @ Y1) @ sK3)))) & (in @ Y0 @ (dsetconstr @ sK4 @ (^[Y1 : $i]: (in @ (kpair @ X0 @ Y1) @ sK3)))))))) = $true) | ($true = ((subset @ sK3 @ (cartprod @ sK2 @ sK4)) & $false))) )),
% 76.61/12.46 inference(beta_eta_normalization,[status(thm)],[f4165])).
% 76.61/12.46 thf(f4165,plain,(
% 76.61/12.46 ( ! [X0 : $i] : (($true = ((subset @ sK3 @ (cartprod @ sK2 @ sK4)) & $false)) | (((^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK3)))) & (in @ Y1 @ (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK3))))))))) @ X0) = $true)) )),
% 76.61/12.46 inference(superposition,[status(thm)],[f1215,f592])).
% 76.61/12.46 thf(f592,plain,(
% 76.61/12.46 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = (!! @ X0 @ X1)) | ($true = (X1 @ X2))) )),
% 76.61/12.46 introduced(definition,[],[pi_proxy_axiom])).
% 76.61/12.46 thf(f3870,plain,(
% 76.61/12.46 spl6_87 | spl6_83 | ~spl6_84),
% 76.61/12.46 inference(avatar_split_clause,[status(thm)],[f3865,f3781,f3759,f3867])).
% 76.61/12.46 thf(f3759,definition,(
% 76.61/12.46 spl6_83 <=> ($true = (!! @ $o @ (=> @ $true)))),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_83])],[avatar_definition])).
% 76.61/12.46 thf(f3781,definition,(
% 76.61/12.46 spl6_84 <=> ($false = (sK0 @ $o @ (=> @ $true)))),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_84])],[avatar_definition])).
% 76.61/12.46 thf(f3865,plain,(
% 76.61/12.46 ($false = ($true => $false)) | (spl6_83 | ~spl6_84)),
% 76.61/12.46 inference(subsumption_resolution,[status(thm)],[f3863,f3760])).
% 76.61/12.46 thf(f3760,plain,(
% 76.61/12.46 ($true != (!! @ $o @ (=> @ $true))) | spl6_83),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f3759])).
% 76.61/12.46 thf(f3863,plain,(
% 76.61/12.46 ($false = ($true => $false)) | ($true = (!! @ $o @ (=> @ $true))) | ~spl6_84),
% 76.61/12.46 inference(superposition,[status(thm)],[f591,f3783])).
% 76.61/12.46 thf(f3783,plain,(
% 76.61/12.46 ($false = (sK0 @ $o @ (=> @ $true))) | ~spl6_84),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f3781])).
% 76.61/12.46 thf(f591,plain,(
% 76.61/12.46 ( ! [X0 : $tType,X1 : X0 > $o] : (((X1 @ (sK0 @ X0 @ X1)) = $false) | ($true = (!! @ X0 @ X1))) )),
% 76.61/12.46 introduced(definition,[],[pi_proxy_axiom])).
% 76.61/12.46 thf(f3841,plain,(
% 76.61/12.46 spl6_23 | ~spl6_85),
% 76.61/12.46 inference(avatar_split_clause,[status(thm)],[f3837,f3799,f1625])).
% 76.61/12.46 thf(f1625,definition,(
% 76.61/12.46 spl6_23 <=> ! [X0 : $o] : ($true = X0)),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_23])],[avatar_definition])).
% 76.61/12.46 thf(f3799,definition,(
% 76.61/12.46 spl6_85 <=> ! [X0 : $o] : ($true = ($true => X0))),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_85])],[avatar_definition])).
% 76.61/12.46 thf(f3837,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = X0)) ) | ~spl6_85),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f3836])).
% 76.61/12.46 thf(f3836,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = X0) | ($true = $false)) ) | ~spl6_85),
% 76.61/12.46 inference(duplicate_literal_removal,[status(thm)],[f3830])).
% 76.61/12.46 thf(f3830,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = X0) | ($true = $false) | ($true = $false)) ) | ~spl6_85),
% 76.61/12.46 inference(superposition,[status(thm)],[f3800,f597])).
% 76.61/12.46 thf(f597,plain,(
% 76.61/12.46 ( ! [X2 : $o,X1 : $o] : (($false = (X1 => X2)) | ($false = X1) | ($true = X2)) )),
% 76.61/12.46 introduced(definition,[],[implies_proxy_axiom])).
% 76.61/12.46 thf(f3800,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = ($true => X0))) ) | ~spl6_85),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f3799])).
% 76.61/12.46 thf(f3802,plain,(
% 76.61/12.46 spl6_85 | ~spl6_83),
% 76.61/12.46 inference(avatar_split_clause,[status(thm)],[f3796,f3759,f3799])).
% 76.61/12.46 thf(f3796,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = ($true => X0))) ) | ~spl6_83),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f3794])).
% 76.61/12.46 thf(f3794,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = ($true => X0)) | ($true = $false)) ) | ~spl6_83),
% 76.61/12.46 inference(superposition,[status(thm)],[f3761,f592])).
% 76.61/12.46 thf(f3761,plain,(
% 76.61/12.46 ($true = (!! @ $o @ (=> @ $true))) | ~spl6_83),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f3759])).
% 76.61/12.46 thf(f3785,plain,(
% 76.61/12.46 spl6_84 | ~spl6_82),
% 76.61/12.46 inference(avatar_split_clause,[status(thm)],[f3777,f3755,f3781])).
% 76.61/12.46 thf(f3755,definition,(
% 76.61/12.46 spl6_82 <=> ($true = ((sK0 @ $o @ (=> @ $true)) => $false))),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_82])],[avatar_definition])).
% 76.61/12.46 thf(f3777,plain,(
% 76.61/12.46 ($false = (sK0 @ $o @ (=> @ $true))) | ~spl6_82),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f3776])).
% 76.61/12.46 thf(f3776,plain,(
% 76.61/12.46 ($false = (sK0 @ $o @ (=> @ $true))) | ($true = $false) | ~spl6_82),
% 76.61/12.46 inference(duplicate_literal_removal,[status(thm)],[f3775])).
% 76.61/12.46 thf(f3775,plain,(
% 76.61/12.46 ($true = $false) | ($false = (sK0 @ $o @ (=> @ $true))) | ($true = $false) | ~spl6_82),
% 76.61/12.46 inference(superposition,[status(thm)],[f597,f3757])).
% 76.61/12.46 thf(f3757,plain,(
% 76.61/12.46 ($true = ((sK0 @ $o @ (=> @ $true)) => $false)) | ~spl6_82),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f3755])).
% 76.61/12.46 thf(f3763,plain,(
% 76.61/12.46 spl6_82 | spl6_83),
% 76.61/12.46 inference(avatar_split_clause,[status(thm)],[f3748,f3759,f3755])).
% 76.61/12.46 thf(f3748,plain,(
% 76.61/12.46 ($true = ((sK0 @ $o @ (=> @ $true)) => $false)) | ($true = (!! @ $o @ (=> @ $true)))),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f3747])).
% 76.61/12.46 thf(f3747,plain,(
% 76.61/12.46 ($true = $false) | ($true = ((sK0 @ $o @ (=> @ $true)) => $false)) | ($true = (!! @ $o @ (=> @ $true)))),
% 76.61/12.46 inference(superposition,[status(thm)],[f591,f3730])).
% 76.61/12.46 thf(f3730,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = ($true => X0)) | ($true = (X0 => $false))) )),
% 76.61/12.46 inference(superposition,[status(thm)],[f1588,f3589])).
% 76.61/12.46 thf(f3589,plain,(
% 76.61/12.46 ( ! [X0 : $i,X1 : $o] : (($false = (in @ X0 @ (prop2set @ X1))) | (($true => X1) = $true)) )),
% 76.61/12.46 inference(fool_paramodulation,[status(thm)],[f3581])).
% 76.61/12.46 thf(f3581,plain,(
% 76.61/12.46 ( ! [X0 : $i,X1 : $o] : (($true = ((in @ X0 @ (prop2set @ X1)) => X1))) )),
% 76.61/12.46 inference(beta_eta_normalization,[status(thm)],[f3580])).
% 76.61/12.46 thf(f3580,plain,(
% 76.61/12.46 ( ! [X0 : $i,X1 : $o] : (($true = ((^[Y0 : $o]: ((in @ X0 @ (prop2set @ Y0)) => Y0)) @ X1))) )),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f3576])).
% 76.61/12.46 thf(f3576,plain,(
% 76.61/12.46 ( ! [X0 : $i,X1 : $o] : (($true = ((^[Y0 : $o]: ((in @ X0 @ (prop2set @ Y0)) => Y0)) @ X1)) | ($true = $false)) )),
% 76.61/12.46 inference(superposition,[status(thm)],[f1801,f592])).
% 76.61/12.46 thf(f1801,plain,(
% 76.61/12.46 ( ! [X0 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: ((in @ X0 @ (prop2set @ Y0)) => Y0))))) )),
% 76.61/12.46 inference(beta_eta_normalization,[status(thm)],[f1800])).
% 76.61/12.46 thf(f1800,plain,(
% 76.61/12.46 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1)))) @ X0))) )),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f1797])).
% 76.61/12.46 thf(f1797,plain,(
% 76.61/12.46 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1)))) @ X0)) | ($true = $false)) )),
% 76.61/12.46 inference(superposition,[status(thm)],[f592,f1126])).
% 76.61/12.46 thf(f1126,plain,(
% 76.61/12.46 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))),
% 76.61/12.46 inference(definition_unfolding,[status(thm)],[f925,f721])).
% 76.61/12.46 thf(f721,plain,(
% 76.61/12.46 (prop2setE = $true)),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f608])).
% 76.61/12.46 thf(f925,plain,(
% 76.61/12.46 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f530])).
% 76.61/12.46 thf(f530,plain,(
% 76.61/12.46 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))),
% 76.61/12.46 inference(fool_elimination,[status(thm)],[f529])).
% 76.61/12.46 thf(f529,plain,(
% 76.61/12.46 (prop2setE = ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 76.61/12.46 inference(rectify,[status(thm)],[f18])).
% 76.61/12.46 thf(f18,axiom,(
% 76.61/12.46 (prop2setE = ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 76.61/12.46 file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',prop2setE)).
% 76.61/12.46 thf(f1588,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = (X0 => (in @ emptyset @ (prop2set @ X0))))) )),
% 76.61/12.46 inference(beta_eta_normalization,[status(thm)],[f1587])).
% 76.61/12.46 thf(f1587,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = ((^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))) @ X0))) )),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f1584])).
% 76.61/12.46 thf(f1584,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = ((^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))) @ X0)) | ($true = $false)) )),
% 76.61/12.46 inference(superposition,[status(thm)],[f592,f1069])).
% 76.61/12.46 thf(f1069,plain,(
% 76.61/12.46 ($true = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 76.61/12.46 inference(definition_unfolding,[status(thm)],[f761,f610])).
% 76.61/12.46 thf(f610,plain,(
% 76.61/12.46 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f540])).
% 76.61/12.46 thf(f540,plain,(
% 76.61/12.46 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 76.61/12.46 inference(fool_elimination,[status(thm)],[f539])).
% 76.61/12.46 thf(f539,plain,(
% 76.61/12.46 (! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))) = prop2setI)),
% 76.61/12.46 inference(rectify,[status(thm)],[f59])).
% 76.61/12.46 thf(f59,axiom,(
% 76.61/12.46 (! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))) = prop2setI)),
% 76.61/12.46 file('/export/starexec/sandbox2/tmp/tmp.ByYgfFFhyN/DTF2THF_17169.p',prop2setI)).
% 76.61/12.46 thf(f761,plain,(
% 76.61/12.46 (prop2setI = $true)),
% 76.61/12.46 inference(cnf_transformation,[status(thm)],[f608])).
% 76.61/12.46 thf(f1668,plain,(
% 76.61/12.46 spl6_19 | ~spl6_23),
% 76.61/12.46 inference(avatar_split_clause,[status(thm)],[f1662,f1625,f1500])).
% 76.61/12.46 thf(f1500,definition,(
% 76.61/12.46 spl6_19 <=> ! [X0 : $o] : ($false = X0)),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_19])],[avatar_definition])).
% 76.61/12.46 thf(f1662,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($false = X0)) ) | ~spl6_23),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f1643])).
% 76.61/12.46 thf(f1643,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = $false) | ($false = X0)) ) | ~spl6_23),
% 76.61/12.46 inference(superposition,[status(thm)],[f590,f1626])).
% 76.61/12.46 thf(f1626,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($true = X0)) ) | ~spl6_23),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f1625])).
% 76.61/12.46 thf(f590,plain,(
% 76.61/12.46 ( ! [X1 : $o] : (($false = (~ X1)) | ($false = X1)) )),
% 76.61/12.46 introduced(definition,[],[logical_not_proxy_axiom])).
% 76.61/12.46 thf(f1654,plain,(
% 76.61/12.46 spl6_4 | ~spl6_23),
% 76.61/12.46 inference(avatar_contradiction_clause,[status(thm)],[f1653])).
% 76.61/12.46 thf(f1653,plain,(
% 76.61/12.46 $false | (spl6_4 | ~spl6_23)),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f1649])).
% 76.61/12.46 thf(f1649,plain,(
% 76.61/12.46 ($true != $true) | (spl6_4 | ~spl6_23)),
% 76.61/12.46 inference(superposition,[status(thm)],[f1362,f1626])).
% 76.61/12.46 thf(f1362,plain,(
% 76.61/12.46 ((!! @ $o @ ~) != $true) | spl6_4),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f1361])).
% 76.61/12.46 thf(f1361,definition,(
% 76.61/12.46 spl6_4 <=> ((!! @ $o @ ~) = $true)),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition])).
% 76.61/12.46 thf(f1536,plain,(
% 76.61/12.46 spl6_18 | ~spl6_19),
% 76.61/12.46 inference(avatar_contradiction_clause,[status(thm)],[f1535])).
% 76.61/12.46 thf(f1535,plain,(
% 76.61/12.46 $false | (spl6_18 | ~spl6_19)),
% 76.61/12.46 inference(subsumption_resolution,[status(thm)],[f1480,f1501])).
% 76.61/12.46 thf(f1501,plain,(
% 76.61/12.46 ( ! [X0 : $o] : (($false = X0)) ) | ~spl6_19),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f1500])).
% 76.61/12.46 thf(f1480,plain,(
% 76.61/12.46 ((!! @ $o @ ~) != $false) | spl6_18),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f1479])).
% 76.61/12.46 thf(f1479,definition,(
% 76.61/12.46 spl6_18 <=> ((!! @ $o @ ~) = $false)),
% 76.61/12.46 introduced(definition,[new_symbols(naming,[spl6_18])],[avatar_definition])).
% 76.61/12.46 thf(f1531,plain,(
% 76.61/12.46 ~spl6_4 | ~spl6_18),
% 76.61/12.46 inference(avatar_contradiction_clause,[status(thm)],[f1530])).
% 76.61/12.46 thf(f1530,plain,(
% 76.61/12.46 $false | (~spl6_4 | ~spl6_18)),
% 76.61/12.46 inference(trivial_inequality_removal,[status(thm)],[f1529])).
% 76.61/12.46 thf(f1529,plain,(
% 76.61/12.46 ($true = $false) | (~spl6_4 | ~spl6_18)),
% 76.61/12.46 inference(forward_demodulation,[status(thm)],[f1363,f1481])).
% 76.61/12.46 thf(f1481,plain,(
% 76.61/12.46 ((!! @ $o @ ~) = $false) | ~spl6_18),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f1479])).
% 76.61/12.46 thf(f1363,plain,(
% 76.61/12.46 ((!! @ $o @ ~) = $true) | ~spl6_4),
% 76.61/12.46 inference(avatar_component_clause,[status(thm)],[f1361])).
% 76.61/12.46 % SZS output end Proof for DTF2THF_17169
% 76.61/12.46 % (17491)------------------------------
% 76.61/12.46 % (17491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.61/12.46 % (17491)Termination reason: Refutation
% 76.61/12.46
% 76.61/12.46 % (17491)Memory used [KB]: 10618
% 76.61/12.46 % (17491)Time elapsed: 0.684 s
% 76.61/12.46 % (17491)Instructions burned: 2279 (million)
% 76.61/12.46 % (17491)------------------------------
% 76.61/12.46 % (17491)------------------------------
% 76.61/12.46 % (17267)Success in time 10.814 s
%------------------------------------------------------------------------------