%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU531^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:50 AM UTC 2026
% Result : Theorem 3.60s 0.84s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 51
% Syntax : Number of formulae : 967 ( 326 unt; 0 typ; 50 def)
% Number of atoms : 8100 (2750 equ; 0 cnn)
% Maximal formula atoms : 50 ( 8 avg)
% Number of connectives : 17711 (4120 ~;3012 |; 88 &;10028 @)
% ( 32 <=>; 431 =>; 0 <=; 0 <~>)
% Maximal formula depth : 56 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 411 ( 411 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 102 usr; 54 con; 0-4 aty)
% Number of variables : 3622 ( 120 ^;3418 !; 84 ?;3622 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_emptyI,type,
emptyI: $o ).
thf(tp_emptyInPowerset,type,
emptyInPowerset: $o ).
thf(tp_emptyinPowerset,type,
emptyinPowerset: $o ).
thf(tp_emptyinunitempty,type,
emptyinunitempty: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_exuE2,type,
exuE2: $o ).
thf(tp_exuE3e,type,
exuE3e: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_noeltsimpempty,type,
noeltsimpempty: $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_nonemptyE1,type,
nonemptyE1: $o ).
thf(tp_nonemptyI,type,
nonemptyI: $o ).
thf(tp_nonemptyI1,type,
nonemptyI1: $o ).
thf(tp_nonemptyImpWitness,type,
nonemptyImpWitness: $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_notinsingleton,type,
notinsingleton: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK10_SY445,type,
sK10_SY445: $i > $i > $i ).
thf(tp_sK11_SY344,type,
sK11_SY344: $i > $i ).
thf(tp_sK12_SY374,type,
sK12_SY374: $i > $i ).
thf(tp_sK13_SY316,type,
sK13_SY316: $i > $i ).
thf(tp_sK14_SY481,type,
sK14_SY481: $o > $i > $i > $i ).
thf(tp_sK15_SX0,type,
sK15_SX0: $i > $i > $i ).
thf(tp_sK16_SX0,type,
sK16_SX0: $i > $i > $i ).
thf(tp_sK17_SY366,type,
sK17_SY366: $i > $i > $i ).
thf(tp_sK18_SY448,type,
sK18_SY448: $i > $i > $i ).
thf(tp_sK19_SY416,type,
sK19_SY416: $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY423,type,
sK20_SY423: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK21_SY446,type,
sK21_SY446: $i > $i > $i ).
thf(tp_sK22_SY446,type,
sK22_SY446: $i > $i > $i ).
thf(tp_sK23_SY476,type,
sK23_SY476: $i > ( $i > $o ) > $i ).
thf(tp_sK24_SY479,type,
sK24_SY479: $i > ( $i > $o ) > $i ).
thf(tp_sK25_SY480,type,
sK25_SY480: $i > ( $i > $o ) > $i ).
thf(tp_sK26_SY482,type,
sK26_SY482: $i > ( $i > $o ) > $i ).
thf(tp_sK27_SY483,type,
sK27_SY483: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK28_SY347,type,
sK28_SY347: $i > ( $i > $o ) > $i ).
thf(tp_sK29_SY351,type,
sK29_SY351: $i > ( $i > $o ) > $i ).
thf(tp_sK2_SY439,type,
sK2_SY439: $i ).
thf(tp_sK30_SY388,type,
sK30_SY388: $i > ( $i > $o ) > $i ).
thf(tp_sK31_SY485,type,
sK31_SY485: $i > $i > $i ).
thf(tp_sK32_SY347,type,
sK32_SY347: $i > ( $i > $o ) > $i ).
thf(tp_sK33_SY351,type,
sK33_SY351: $i > ( $i > $o ) > $i ).
thf(tp_sK34_SY388,type,
sK34_SY388: $i > ( $i > $o ) > $i ).
thf(tp_sK35_SY423,type,
sK35_SY423: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK36_SY495,type,
sK36_SY495: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK37_SY423,type,
sK37_SY423: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK38_SY487,type,
sK38_SY487: $i > $i > $i > $i ).
thf(tp_sK39_SY487,type,
sK39_SY487: $i > $i > $i > $i ).
thf(tp_sK3_SY390,type,
sK3_SY390: $i > $i ).
thf(tp_sK40_SY509,type,
sK40_SY509: $i > $i > $i > $i ).
thf(tp_sK41_SY520,type,
sK41_SY520: $i > $i > $i > $i ).
thf(tp_sK42_SY524,type,
sK42_SY524: $i > $i > $i > $i ).
thf(tp_sK43_SY516,type,
sK43_SY516: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK44_SY518,type,
sK44_SY518: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK4_SY456,type,
sK4_SY456: $i ).
thf(tp_sK5_SY375,type,
sK5_SY375: $i > $i ).
thf(tp_sK6_SY376,type,
sK6_SY376: $i > $i ).
thf(tp_sK7_SY418,type,
sK7_SY418: $i > $i > $i ).
thf(tp_sK8_SY420,type,
sK8_SY420: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK9_SY429,type,
sK9_SY429: $i > $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setadjoinIR,type,
setadjoinIR: $o ).
thf(tp_setadjoinOr,type,
setadjoinOr: $o ).
thf(tp_setbeta,type,
setbeta: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setoftrueEq,type,
setoftrueEq: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_singletonsswitch,type,
singletonsswitch: $o ).
thf(tp_subPowSU,type,
subPowSU: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(prop2set,definition,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,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
=> ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(2,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
=> ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY20: $i > $i > $o,SY21: $i] :
( ! [SY22: $i] :
( ( in @ SY22 @ SY21 )
=> ? [SY24: $i] :
( ( SY20 @ SY22 @ SY24 )
& ! [SY25: $i] :
( ( SY20 @ SY22 @ SY25 )
=> ( SY24 = SY25 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY21 )
& ( SY20 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) )
=> ( ! [SY52: $i > $o] :
( ? [SY54: $i] :
( ( SY52 @ SY54 )
& ! [SY55: $i] :
( ( SY52 @ SY55 )
=> ( SY54 = SY55 ) ) )
=> ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY69: $i > $o] :
( ? [SY71: $i] :
( ( SY69 @ SY71 )
& ! [SY72: $i] :
( ( SY69 @ SY72 )
=> ( SY71 = SY72 ) ) )
=> ? [Xx: $i] :
( ( SY69 @ Xx )
& ! [Xy: $i] :
( ( SY69 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY75: $o,SY76: $i] :
( ( in @ SY76
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY77: $i] : SY75 ) )
=> SY75 )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY82: $i > $o] :
( ? [SY84: $i] :
( ( SY82 @ SY84 )
& ! [SY85: $i] :
( ( SY82 @ SY85 )
=> ( SY84 = SY85 ) ) )
=> ? [Xx: $i] : ( SY82 @ Xx ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) )
=> ( ! [SY99: $i] :
( ( SY99 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY99 ) )
=> ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ( in @ SY103 @ SY101 )
=> ( ( SY102 @ SY103 )
=> ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY105: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY105 )
=> ( SY105 != emptyset ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) )
=> ( ! [SY138: $i > $o] :
( ? [SY140: $i] :
( ( SY138 @ SY140 )
& ! [SY141: $i] :
( ( SY138 @ SY141 )
=> ( SY140 = SY141 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY138 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY144: $i] :
( ( SY144 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY144 )
& $true ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [SY20: $i > $i > $o,SY21: $i] :
( ! [SY22: $i] :
( ( in @ SY22 @ SY21 )
=> ? [SY24: $i] :
( ( SY20 @ SY22 @ SY24 )
& ! [SY25: $i] :
( ( SY20 @ SY22 @ SY25 )
=> ( SY24 = SY25 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY21 )
& ( SY20 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY52: $i > $o] :
( ? [SY54: $i] :
( ( SY52 @ SY54 )
& ! [SY55: $i] :
( ( SY52 @ SY55 )
=> ( SY54 = SY55 ) ) )
=> ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY69: $i > $o] :
( ? [SY71: $i] :
( ( SY69 @ SY71 )
& ! [SY72: $i] :
( ( SY69 @ SY72 )
=> ( SY71 = SY72 ) ) )
=> ? [Xx: $i] :
( ( SY69 @ Xx )
& ! [Xy: $i] :
( ( SY69 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [SY75: $o,SY76: $i] :
( ( in @ SY76
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY77: $i] : SY75 ) )
=> SY75 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY82: $i > $o] :
( ? [SY84: $i] :
( ( SY82 @ SY84 )
& ! [SY85: $i] :
( ( SY82 @ SY85 )
=> ( SY84 = SY85 ) ) )
=> ? [Xx: $i] : ( SY82 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [SY99: $i] :
( ( SY99 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY99 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ( in @ SY103 @ SY101 )
=> ( ( SY102 @ SY103 )
=> ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY105: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY105 )
=> ( SY105 != emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [SY138: $i > $o] :
( ? [SY140: $i] :
( ( SY138 @ SY140 )
& ! [SY141: $i] :
( ( SY138 @ SY141 )
=> ( SY140 = SY141 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY138 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY144: $i] :
( ( SY144 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY144 )
& $true ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(47,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(49,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(52,plain,
( ( ~ ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[51]) ).
thf(53,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(54,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(55,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(56,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(57,plain,
( ( ! [SY144: $i] :
( ( SY144 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY144 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(58,plain,
( ( ! [SY138: $i > $o] :
( ? [SY140: $i] :
( ( SY138 @ SY140 )
& ! [SY141: $i] :
( ( SY138 @ SY141 )
=> ( SY140 = SY141 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY138 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(59,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(60,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(61,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(62,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(63,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(64,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(67,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(68,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(69,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(70,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(71,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(72,plain,
( ( ! [SY105: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY105 )
=> ( SY105 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(73,plain,
( ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ( in @ SY103 @ SY101 )
=> ( ( SY102 @ SY103 )
=> ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(74,plain,
( ( ! [SY99: $i] :
( ( SY99 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY99 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(75,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(76,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(77,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(79,plain,
( ( ! [SY82: $i > $o] :
( ? [SY84: $i] :
( ( SY82 @ SY84 )
& ! [SY85: $i] :
( ( SY82 @ SY85 )
=> ( SY84 = SY85 ) ) )
=> ? [Xx: $i] : ( SY82 @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(80,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(81,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(82,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(83,plain,
( ( ! [SY75: $o,SY76: $i] :
( ( in @ SY76
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY77: $i] : SY75 ) )
=> SY75 ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(84,plain,
( ( ! [SY69: $i > $o] :
( ? [SY71: $i] :
( ( SY69 @ SY71 )
& ! [SY72: $i] :
( ( SY69 @ SY72 )
=> ( SY71 = SY72 ) ) )
=> ? [Xx: $i] :
( ( SY69 @ Xx )
& ! [Xy: $i] :
( ( SY69 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(85,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(86,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(87,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(88,plain,
( ( ! [SY52: $i > $o] :
( ? [SY54: $i] :
( ( SY52 @ SY54 )
& ! [SY55: $i] :
( ( SY52 @ SY55 )
=> ( SY54 = SY55 ) ) )
=> ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(89,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(90,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(91,plain,
( ( ! [SY20: $i > $i > $o,SY21: $i] :
( ! [SY22: $i] :
( ( in @ SY22 @ SY21 )
=> ? [SY24: $i] :
( ( SY20 @ SY22 @ SY24 )
& ! [SY25: $i] :
( ( SY20 @ SY22 @ SY25 )
=> ( SY24 = SY25 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY21 )
& ( SY20 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(92,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(93,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(94,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(95,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(97,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(98,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(100,plain,
( ( ~ ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(102,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(103,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX2: $i] : SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[83,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(104,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( in @ emptyset @ SX0 )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ( in @ SX1 @ omega )
| ~ ( in @ SX1 @ SX0 ) )
| ( in @ ( setadjoin @ SX1 @ SX1 ) @ SX0 ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(106,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(108,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(110,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( SX0 @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( SX0 @ SX2 @ SX4 )
| ( SX3 = SX4 ) ) ) )
| ~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) )
| ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(115,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(116,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(117,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX2 = SX1 ) )
| ~ ( ( SX2 != SX1 )
| ( SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX1 @ SX3 )
| ~ ( in @ SX3 @ SX0 )
| SX2 )
| SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(124,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(125,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ( SX2 != SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(128,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(129,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(130,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(131,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[81,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(132,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(133,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(134,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(136,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(138,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX4 )
| ( in @ SX3 @ SX4 ) )
| ~ ( ~ ( in @ SX3 @ SX4 )
| ( in @ SX2 @ SX4 ) ) ) )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX2 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SX2 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(139,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[82,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,wellorderingAx]) ).
thf(141,plain,
! [SV1: $i] :
( ( in @ emptyset @ ( powerset @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(142,plain,
! [SV2: $i] :
( ( in @ emptyset @ ( powerset @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(143,plain,
! [SV3: $i] :
( ( ( dsetconstr @ SV3
@ ^ [Xx: $i] : $true )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(144,plain,
! [SV4: $i] :
( ( ! [SY307: $i] : ( in @ SV4 @ ( setadjoin @ SV4 @ SY307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(145,plain,
! [SV5: $i] :
( ( ~ ( in @ SV5 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(146,plain,
! [SV6: $i] :
( ( ~ ( in @ SV6 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(147,plain,
! [SV7: $i] :
( ( ! [SY308: $i > $o,SY309: $i] :
( ~ ( in @ SY309
@ ( dsetconstr @ SV7
@ ^ [SX3: $i] : ( SY308 @ SX3 ) ) )
| ( in @ SY309 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(148,plain,
! [SV8: $i > $o] :
( ( ~ ~ ! [SY311: $i] :
~ ~ ( ~ ( SV8 @ SY311 )
| ~ ! [SY312: $i] :
( ~ ( SV8 @ SY312 )
| ( SY311 = SY312 ) ) )
| ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(149,plain,
! [SV9: $o] :
( ( ! [SY314: $i] :
( ~ ( in @ SY314
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY315: $i] : SV9 ) )
| SV9 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[103]) ).
thf(150,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[103]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[103]) ).
thf(152,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV10 )
| ~ ! [SY316: $i] :
( ~ ~ ( ~ ( in @ SY316 @ omega )
| ~ ( in @ SY316 @ SV10 ) )
| ( in @ ( setadjoin @ SY316 @ SY316 ) @ SV10 ) ) )
| ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(153,plain,
! [SV11: $i] :
( ( ! [SY318: $i] :
~ ( ~ ( ~ ( in @ SY318 @ ( setunion @ SV11 ) )
| ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ SY318 @ SY319 )
| ~ ( in @ SY319 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY320: $i] :
~ ~ ( ~ ( in @ SY318 @ SY320 )
| ~ ( in @ SY320 @ SV11 ) )
| ( in @ SY318 @ ( setunion @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(154,plain,
! [SV12: $i] :
( ( ~ ( in @ SV12 @ omega )
| ( in @ ( setadjoin @ SV12 @ SV12 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(155,plain,
! [SV13: $i] :
( ( ! [SY321: $i] :
( ~ ! [SY322: $i] :
~ ( ~ ( ~ ( in @ SY322 @ SV13 )
| ( in @ SY322 @ SY321 ) )
| ~ ( ~ ( in @ SY322 @ SY321 )
| ( in @ SY322 @ SV13 ) ) )
| ( SV13 = SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(156,plain,
! [SV14: $i] :
( ( ~ ~ ! [SY323: $i] :
~ ( in @ SY323 @ SV14 )
| ( SV14 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(157,plain,
! [SV15: $i] :
( ( ! [SY324: $i,SY325: $i] :
~ ( ~ ( ~ ( in @ SY325 @ ( setadjoin @ SV15 @ SY324 ) )
| ( SY325 = SV15 )
| ( in @ SY325 @ SY324 ) )
| ~ ( ~ ( ( SY325 = SV15 )
| ( in @ SY325 @ SY324 ) )
| ( in @ SY325 @ ( setadjoin @ SV15 @ SY324 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(158,plain,
! [SV16: $i > $i > $o] :
( ( ! [SY326: $i] :
( ~ ! [SY327: $i] :
( ~ ( in @ SY327 @ SY326 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( SV16 @ SY327 @ SY328 )
| ~ ! [SY329: $i] :
( ~ ( SV16 @ SY327 @ SY329 )
| ( SY328 = SY329 ) ) ) )
| ~ ! [SY330: $i] :
~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SY330 )
| ~ ! [SY332: $i] :
~ ~ ( ~ ( in @ SY332 @ SY326 )
| ~ ( SV16 @ SY332 @ SY331 ) ) )
| ~ ( ~ ~ ! [SY333: $i] :
~ ~ ( ~ ( in @ SY333 @ SY326 )
| ~ ( SV16 @ SY333 @ SY331 ) )
| ( in @ SY331 @ SY330 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(159,plain,
! [SV17: $i] :
( ( ! [SY334: $i > $o,SY335: $i] :
( ~ ( in @ SY335 @ SV17 )
| ~ ( SY334 @ SY335 )
| ( ( dsetconstr @ SV17
@ ^ [SX3: $i] : ( SY334 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(160,plain,
! [SV18: $i] :
( ( ! [SY337: $i] :
( ~ ! [SY338: $i] :
( ~ ( in @ SY338 @ SY337 )
| ( in @ SY338 @ SV18 ) )
| ( in @ SY337 @ ( powerset @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(161,plain,
! [SV19: $i] :
( ( ! [SY339: $i] :
( ~ ( in @ SV19 @ ( setadjoin @ SY339 @ emptyset ) )
| ( in @ SY339 @ ( setadjoin @ SV19 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(162,plain,
! [SV20: $i] :
( ( ! [SY340: $i > $o,SY341: $i] :
( ~ ( in @ SY341 @ SV20 )
| ~ ( ~ ( ~ ( in @ SY341
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY340 @ SX3 ) ) )
| ( SY340 @ SY341 ) )
| ~ ( ~ ( SY340 @ SY341 )
| ( in @ SY341
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY340 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(163,plain,
! [SV21: $i] :
( ( ~ ( ( SV21 != emptyset ) )
| ~ ! [SY344: $i] :
~ ( in @ SY344 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(164,plain,
! [SV22: $i > $o] :
( ( ~ ~ ! [SY345: $i] :
~ ~ ( ~ ( SV22 @ SY345 )
| ~ ! [SY346: $i] :
( ~ ( SV22 @ SY346 )
| ( SY345 = SY346 ) ) )
| ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(165,plain,
! [SV23: $i > $o] :
( ( ~ ~ ! [SY349: $i] :
~ ~ ( ~ ( SV23 @ SY349 )
| ~ ! [SY350: $i] :
( ~ ( SV23 @ SY350 )
| ( SY349 = SY350 ) ) )
| ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(166,plain,
! [SV24: $i] :
( ( ! [SY353: $i > $o,SY354: $i] :
( ~ ( in @ SY354 @ SV24 )
| ~ ( SY353 @ SY354 )
| ( in @ SY354
@ ( dsetconstr @ SV24
@ ^ [SX3: $i] : ( SY353 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(167,plain,
! [SV25: $i] :
( ( ! [SY356: $i,SY357: $i] :
( ~ ( in @ SY356 @ SY357 )
| ~ ( in @ SY357 @ SV25 )
| ( in @ SY356 @ ( setunion @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(168,plain,
! [SV26: $i] :
( ( ! [SY358: $i] :
( ~ ( in @ SY358 @ SV26 )
| ( in @ SY358 @ ( powerset @ ( setunion @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(169,plain,
! [SV27: $i] :
( ( ! [SY359: $i] :
( ~ ( in @ SY359 @ ( setunion @ SV27 ) )
| ! [SY360: $o] :
( ~ ! [SY361: $i] :
( ~ ( in @ SY359 @ SY361 )
| ~ ( in @ SY361 @ SV27 )
| SY360 )
| SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(170,plain,
! [SV28: $i] :
( ( ! [SY362: $i] :
( ~ ( ( SV28 != SY362 ) )
| ~ ( in @ SY362 @ ( setadjoin @ SV28 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(171,plain,
! [SV29: $i] :
( ( ! [SY363: $i,SY364: $i] :
( ~ ( in @ SY364 @ ( setadjoin @ SV29 @ SY363 ) )
| ( SY364 = SV29 )
| ( in @ SY364 @ SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(172,plain,
! [SV30: $i] :
( ( ~ ~ ! [SY365: $i] :
~ ( in @ SY365 @ SV30 )
| ~ ! [SY366: $i] :
~ ~ ( ~ ( in @ SY366 @ SV30 )
| ~ ~ ~ ! [SY367: $i] :
~ ~ ( ~ ( in @ SY367 @ SY366 )
| ~ ( in @ SY367 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(174,plain,
! [SV31: $i] :
( ( ! [SY368: $i > $o,SY369: $i] :
( ~ ( in @ SY369
@ ( dsetconstr @ SV31
@ ^ [SX3: $i] : ( SY368 @ SX3 ) ) )
| ( SY368 @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(175,plain,
! [SV32: $i] :
( ( ! [SY371: $i,SY372: $i] :
( ~ ( in @ SY372 @ ( setadjoin @ SV32 @ SY371 ) )
| ! [SY373: $o] :
( ~ ( ( SY372 != SV32 )
| SY373 )
| ~ ( ~ ( in @ SY372 @ SY371 )
| SY373 )
| SY373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(176,plain,
! [SV33: $i] :
( ( ~ ( ( SV33 != emptyset ) )
| ~ ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ SV33 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(177,plain,
! [SV34: $i] :
( ( ~ ! [SY375: $i] :
~ ( in @ SY375 @ SV34 )
| ( SV34 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(178,plain,
! [SV35: $i] :
( ( ~ ! [SY376: $i] :
~ ( in @ SY376 @ SV35 )
| ( SV35 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(179,plain,
! [SV36: $i] :
( ( ~ ( in @ SV36 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(180,plain,
! [SV37: $i] :
( ( ! [SY377: $i] :
( ~ ! [SY378: $i] :
( ~ ( in @ SY378 @ SV37 )
| ( in @ SY378 @ SY377 ) )
| ~ ! [SY379: $i] :
( ~ ( in @ SY379 @ SY377 )
| ( in @ SY379 @ SV37 ) )
| ( SV37 = SY377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(181,plain,
! [SV38: $i] :
( ( ! [SY380: $i] :
( ( SV38 != SY380 )
| ( in @ SV38 @ ( setadjoin @ SY380 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(182,plain,
! [SV39: $i] :
( ( ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ ( powerset @ SV39 ) )
| ! [SY382: $i] :
( ~ ( in @ SY382 @ SY381 )
| ( in @ SY382 @ SV39 ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( in @ SY383 @ SY381 )
| ( in @ SY383 @ SV39 ) )
| ( in @ SY381 @ ( powerset @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(183,plain,
! [SV40: $i] :
( ( ! [SY384: $i,SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( setadjoin @ SV40 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(184,plain,
! [SV41: $i > $o] :
( ( ~ ~ ! [SY386: $i] :
~ ~ ( ~ ( SV41 @ SY386 )
| ~ ! [SY387: $i] :
( ~ ( SV41 @ SY387 )
| ( SY386 = SY387 ) ) )
| ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(185,plain,
! [SV42: $i] :
( ( ! [SY389: $i] :
( ~ ( in @ SV42 @ ( setadjoin @ SY389 @ emptyset ) )
| ( SV42 = SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(186,plain,
! [SV43: $i] :
( ( ~ ! [SY390: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY391: $i] :
( ~ ( in @ SY391 @ SY390 )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY391 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY393: $i,SY394: $i] :
( ~ ~ ( ~ ( in @ SY393 @ SV43 )
| ~ ( in @ SY394 @ SV43 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY390 )
| ~ ( ~ ( ~ ( in @ SY393 @ SX4 )
| ( in @ SY394 @ SX4 ) )
| ~ ( ~ ( in @ SY394 @ SX4 )
| ( in @ SY393 @ SX4 ) ) ) )
| ( SY393 = SY394 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY390 )
| ~ ( in @ SX3 @ SY390 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY400: $i] :
( ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY400 )
| ( in @ SY401 @ SV43 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY400 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY390 )
| ~ ( in @ SX4 @ SY400 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY400 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY390 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(187,plain,
! [SV44: $i] :
( ( ~ ( in @ SV44 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(188,plain,
! [SV45: $i] :
( ( ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( powerset @ SV45 ) )
| ~ ( in @ SY410 @ SY409 )
| ( in @ SY410 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(189,plain,
! [SV46: $i,SV4: $i] :
( ( in @ SV4 @ ( setadjoin @ SV4 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(190,plain,
! [SV5: $i] :
( ( in @ SV5 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(191,plain,
! [SV6: $i] :
( ( in @ SV6 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(192,plain,
! [SV47: $i > $o,SV7: $i] :
( ( ! [SY411: $i] :
( ~ ( in @ SY411
@ ( dsetconstr @ SV7
@ ^ [SY412: $i] : ( SV47 @ SY412 ) ) )
| ( in @ SY411 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(193,plain,
! [SV8: $i > $o] :
( ( ( ~ ~ ! [SY311: $i] :
~ ~ ( ~ ( SV8 @ SY311 )
| ~ ! [SY312: $i] :
( ~ ( SV8 @ SY312 )
| ( SY311 = SY312 ) ) ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(194,plain,
! [SV9: $o,SV48: $i] :
( ( ~ ( in @ SV48
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY315: $i] : SV9 ) )
| SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(195,plain,
! [SV49: $i] :
( ( ~ ( in @ SV49
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(196,plain,
! [SV50: $i] :
( ( ~ ( in @ SV50
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(197,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV10 )
| ~ ! [SY316: $i] :
( ~ ~ ( ~ ( in @ SY316 @ omega )
| ~ ( in @ SY316 @ SV10 ) )
| ( in @ ( setadjoin @ SY316 @ SY316 ) @ SV10 ) ) ) )
= $true )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(198,plain,
! [SV11: $i,SV51: $i] :
( ( ~ ( ~ ( ~ ( in @ SV51 @ ( setunion @ SV11 ) )
| ~ ! [SY416: $i] :
~ ~ ( ~ ( in @ SV51 @ SY416 )
| ~ ( in @ SY416 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( in @ SV51 @ SY417 )
| ~ ( in @ SY417 @ SV11 ) )
| ( in @ SV51 @ ( setunion @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(199,plain,
! [SV12: $i] :
( ( ( ~ ( in @ SV12 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV12 @ SV12 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(200,plain,
! [SV52: $i,SV13: $i] :
( ( ~ ! [SY418: $i] :
~ ( ~ ( ~ ( in @ SY418 @ SV13 )
| ( in @ SY418 @ SV52 ) )
| ~ ( ~ ( in @ SY418 @ SV52 )
| ( in @ SY418 @ SV13 ) ) )
| ( SV13 = SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(201,plain,
! [SV14: $i] :
( ( ( ~ ~ ! [SY323: $i] :
~ ( in @ SY323 @ SV14 ) )
= $true )
| ( ( SV14 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(202,plain,
! [SV53: $i,SV15: $i] :
( ( ! [SY419: $i] :
~ ( ~ ( ~ ( in @ SY419 @ ( setadjoin @ SV15 @ SV53 ) )
| ( SY419 = SV15 )
| ( in @ SY419 @ SV53 ) )
| ~ ( ~ ( ( SY419 = SV15 )
| ( in @ SY419 @ SV53 ) )
| ( in @ SY419 @ ( setadjoin @ SV15 @ SV53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(203,plain,
! [SV16: $i > $i > $o,SV54: $i] :
( ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV54 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( SV16 @ SY420 @ SY328 )
| ~ ! [SY329: $i] :
( ~ ( SV16 @ SY420 @ SY329 )
| ( SY328 = SY329 ) ) ) )
| ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(204,plain,
! [SV55: $i > $o,SV17: $i] :
( ( ! [SY427: $i] :
( ~ ( in @ SY427 @ SV17 )
| ~ ( SV55 @ SY427 )
| ( ( dsetconstr @ SV17
@ ^ [SY428: $i] : ( SV55 @ SY428 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(205,plain,
! [SV18: $i,SV56: $i] :
( ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV56 )
| ( in @ SY429 @ SV18 ) )
| ( in @ SV56 @ ( powerset @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(206,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ( in @ SV19 @ ( setadjoin @ SV57 @ emptyset ) )
| ( in @ SV57 @ ( setadjoin @ SV19 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(207,plain,
! [SV58: $i > $o,SV20: $i] :
( ( ! [SY430: $i] :
( ~ ( in @ SY430 @ SV20 )
| ~ ( ~ ( ~ ( in @ SY430
@ ( dsetconstr @ SV20
@ ^ [SY431: $i] : ( SV58 @ SY431 ) ) )
| ( SV58 @ SY430 ) )
| ~ ( ~ ( SV58 @ SY430 )
| ( in @ SY430
@ ( dsetconstr @ SV20
@ ^ [SY432: $i] : ( SV58 @ SY432 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(208,plain,
! [SV21: $i] :
( ( ( ~ ( ( SV21 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY344: $i] :
~ ( in @ SY344 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(209,plain,
! [SV22: $i > $o] :
( ( ( ~ ~ ! [SY345: $i] :
~ ~ ( ~ ( SV22 @ SY345 )
| ~ ! [SY346: $i] :
( ~ ( SV22 @ SY346 )
| ( SY345 = SY346 ) ) ) )
= $true )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(210,plain,
! [SV23: $i > $o] :
( ( ( ~ ~ ! [SY349: $i] :
~ ~ ( ~ ( SV23 @ SY349 )
| ~ ! [SY350: $i] :
( ~ ( SV23 @ SY350 )
| ( SY349 = SY350 ) ) ) )
= $true )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(211,plain,
! [SV59: $i > $o,SV24: $i] :
( ( ! [SY433: $i] :
( ~ ( in @ SY433 @ SV24 )
| ~ ( SV59 @ SY433 )
| ( in @ SY433
@ ( dsetconstr @ SV24
@ ^ [SY434: $i] : ( SV59 @ SY434 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(212,plain,
! [SV25: $i,SV60: $i] :
( ( ! [SY435: $i] :
( ~ ( in @ SV60 @ SY435 )
| ~ ( in @ SY435 @ SV25 )
| ( in @ SV60 @ ( setunion @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(213,plain,
! [SV26: $i,SV61: $i] :
( ( ~ ( in @ SV61 @ SV26 )
| ( in @ SV61 @ ( powerset @ ( setunion @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(214,plain,
! [SV27: $i,SV62: $i] :
( ( ~ ( in @ SV62 @ ( setunion @ SV27 ) )
| ! [SY436: $o] :
( ~ ! [SY437: $i] :
( ~ ( in @ SV62 @ SY437 )
| ~ ( in @ SY437 @ SV27 )
| SY436 )
| SY436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(215,plain,
! [SV63: $i,SV28: $i] :
( ( ~ ( ( SV28 != SV63 ) )
| ~ ( in @ SV63 @ ( setadjoin @ SV28 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(216,plain,
! [SV64: $i,SV29: $i] :
( ( ! [SY438: $i] :
( ~ ( in @ SY438 @ ( setadjoin @ SV29 @ SV64 ) )
| ( SY438 = SV29 )
| ( in @ SY438 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(217,plain,
! [SV30: $i] :
( ( ( ~ ~ ! [SY365: $i] :
~ ( in @ SY365 @ SV30 ) )
= $true )
| ( ( ~ ! [SY366: $i] :
~ ~ ( ~ ( in @ SY366 @ SV30 )
| ~ ~ ~ ! [SY367: $i] :
~ ~ ( ~ ( in @ SY367 @ SY366 )
| ~ ( in @ SY367 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(218,plain,
( ( ! [SY439: $i,SY440: $i] :
( ~ ( in @ SY440 @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY439 @ emptyset ) ) )
| ( SY440 = sK1_SX0 )
| ( SY440 = SY439 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[173]) ).
thf(219,plain,
! [SV65: $i > $o,SV31: $i] :
( ( ! [SY441: $i] :
( ~ ( in @ SY441
@ ( dsetconstr @ SV31
@ ^ [SY442: $i] : ( SV65 @ SY442 ) ) )
| ( SV65 @ SY441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(220,plain,
! [SV66: $i,SV32: $i] :
( ( ! [SY443: $i] :
( ~ ( in @ SY443 @ ( setadjoin @ SV32 @ SV66 ) )
| ! [SY444: $o] :
( ~ ( ( SY443 != SV32 )
| SY444 )
| ~ ( ~ ( in @ SY443 @ SV66 )
| SY444 )
| SY444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(221,plain,
! [SV33: $i] :
( ( ( ~ ( ( SV33 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ SV33 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(222,plain,
! [SV34: $i] :
( ( ( ~ ! [SY375: $i] :
~ ( in @ SY375 @ SV34 ) )
= $true )
| ( ( SV34 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(223,plain,
! [SV35: $i] :
( ( ( ~ ! [SY376: $i] :
~ ( in @ SY376 @ SV35 ) )
= $true )
| ( ( SV35 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(224,plain,
! [SV36: $i] :
( ( ( ~ ( in @ SV36 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(225,plain,
! [SV67: $i,SV37: $i] :
( ( ~ ! [SY445: $i] :
( ~ ( in @ SY445 @ SV37 )
| ( in @ SY445 @ SV67 ) )
| ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) )
| ( SV37 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(226,plain,
! [SV68: $i,SV38: $i] :
( ( ( SV38 != SV68 )
| ( in @ SV38 @ ( setadjoin @ SV68 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(227,plain,
! [SV39: $i,SV69: $i] :
( ( ~ ( ~ ( ~ ( in @ SV69 @ ( powerset @ SV39 ) )
| ! [SY447: $i] :
( ~ ( in @ SY447 @ SV69 )
| ( in @ SY447 @ SV39 ) ) )
| ~ ( ~ ! [SY448: $i] :
( ~ ( in @ SY448 @ SV69 )
| ( in @ SY448 @ SV39 ) )
| ( in @ SV69 @ ( powerset @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(228,plain,
! [SV40: $i,SV70: $i] :
( ( ! [SY449: $i] :
( ~ ( in @ SY449 @ SV70 )
| ( in @ SY449 @ ( setadjoin @ SV40 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(229,plain,
! [SV41: $i > $o] :
( ( ( ~ ~ ! [SY386: $i] :
~ ~ ( ~ ( SV41 @ SY386 )
| ~ ! [SY387: $i] :
( ~ ( SV41 @ SY387 )
| ( SY386 = SY387 ) ) ) )
= $true )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(230,plain,
! [SV71: $i,SV42: $i] :
( ( ~ ( in @ SV42 @ ( setadjoin @ SV71 @ emptyset ) )
| ( SV42 = SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(231,plain,
! [SV43: $i] :
( ( ! [SY390: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY391: $i] :
( ~ ( in @ SY391 @ SY390 )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY391 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY393: $i,SY394: $i] :
( ~ ~ ( ~ ( in @ SY393 @ SV43 )
| ~ ( in @ SY394 @ SV43 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY390 )
| ~ ( ~ ( ~ ( in @ SY393 @ SX4 )
| ( in @ SY394 @ SX4 ) )
| ~ ( ~ ( in @ SY394 @ SX4 )
| ( in @ SY393 @ SX4 ) ) ) )
| ( SY393 = SY394 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY390 )
| ~ ( in @ SX3 @ SY390 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY400: $i] :
( ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY400 )
| ( in @ SY401 @ SV43 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY400 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY390 )
| ~ ( in @ SX4 @ SY400 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY400 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY390 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(232,plain,
! [SV44: $i] :
( ( ( ~ ( in @ SV44 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(233,plain,
! [SV45: $i,SV72: $i] :
( ( ! [SY450: $i] :
( ~ ( in @ SV72 @ ( powerset @ SV45 ) )
| ~ ( in @ SY450 @ SV72 )
| ( in @ SY450 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(234,plain,
! [SV47: $i > $o,SV7: $i,SV73: $i] :
( ( ~ ( in @ SV73
@ ( dsetconstr @ SV7
@ ^ [SY412: $i] : ( SV47 @ SY412 ) ) )
| ( in @ SV73 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(235,plain,
! [SV8: $i > $o] :
( ( ( ~ ! [SY311: $i] :
~ ~ ( ~ ( SV8 @ SY311 )
| ~ ! [SY312: $i] :
( ~ ( SV8 @ SY312 )
| ( SY311 = SY312 ) ) ) )
= $false )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(236,plain,
! [SV9: $o,SV48: $i] :
( ( ( ~ ( in @ SV48
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY315: $i] : SV9 ) ) )
= $true )
| ( SV9 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(237,plain,
! [SV49: $i] :
( ( ( ~ ( in @ SV49
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(238,plain,
! [SV50: $i] :
( ( ( ~ ( in @ SV50
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(239,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV10 )
| ~ ! [SY316: $i] :
( ~ ~ ( ~ ( in @ SY316 @ omega )
| ~ ( in @ SY316 @ SV10 ) )
| ( in @ ( setadjoin @ SY316 @ SY316 ) @ SV10 ) ) ) )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(240,plain,
! [SV11: $i,SV51: $i] :
( ( ~ ( ~ ( in @ SV51 @ ( setunion @ SV11 ) )
| ~ ! [SY416: $i] :
~ ~ ( ~ ( in @ SV51 @ SY416 )
| ~ ( in @ SY416 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( in @ SV51 @ SY417 )
| ~ ( in @ SY417 @ SV11 ) )
| ( in @ SV51 @ ( setunion @ SV11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(241,plain,
! [SV12: $i] :
( ( ( in @ SV12 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV12 @ SV12 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(242,plain,
! [SV52: $i,SV13: $i] :
( ( ( ~ ! [SY418: $i] :
~ ( ~ ( ~ ( in @ SY418 @ SV13 )
| ( in @ SY418 @ SV52 ) )
| ~ ( ~ ( in @ SY418 @ SV52 )
| ( in @ SY418 @ SV13 ) ) ) )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(243,plain,
! [SV14: $i] :
( ( ( ~ ! [SY323: $i] :
~ ( in @ SY323 @ SV14 ) )
= $false )
| ( ( SV14 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(244,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ~ ( ~ ( ~ ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
| ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
| ~ ( ~ ( ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
| ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(245,plain,
! [SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV54 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( SV16 @ SY420 @ SY328 )
| ~ ! [SY329: $i] :
( ~ ( SV16 @ SY420 @ SY329 )
| ( SY328 = SY329 ) ) ) ) )
= $true )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(246,plain,
! [SV55: $i > $o,SV17: $i,SV75: $i] :
( ( ~ ( in @ SV75 @ SV17 )
| ~ ( SV55 @ SV75 )
| ( ( dsetconstr @ SV17
@ ^ [SY428: $i] : ( SV55 @ SY428 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(247,plain,
! [SV18: $i,SV56: $i] :
( ( ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV56 )
| ( in @ SY429 @ SV18 ) ) )
= $true )
| ( ( in @ SV56 @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(248,plain,
! [SV57: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( setadjoin @ SV57 @ emptyset ) ) )
= $true )
| ( ( in @ SV57 @ ( setadjoin @ SV19 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(249,plain,
! [SV58: $i > $o,SV20: $i,SV76: $i] :
( ( ~ ( in @ SV76 @ SV20 )
| ~ ( ~ ( ~ ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY431: $i] : ( SV58 @ SY431 ) ) )
| ( SV58 @ SV76 ) )
| ~ ( ~ ( SV58 @ SV76 )
| ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY432: $i] : ( SV58 @ SY432 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(250,plain,
! [SV21: $i] :
( ( ( SV21 != emptyset )
= $false )
| ( ( ~ ! [SY344: $i] :
~ ( in @ SY344 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(251,plain,
! [SV22: $i > $o] :
( ( ( ~ ! [SY345: $i] :
~ ~ ( ~ ( SV22 @ SY345 )
| ~ ! [SY346: $i] :
( ~ ( SV22 @ SY346 )
| ( SY345 = SY346 ) ) ) )
= $false )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(252,plain,
! [SV23: $i > $o] :
( ( ( ~ ! [SY349: $i] :
~ ~ ( ~ ( SV23 @ SY349 )
| ~ ! [SY350: $i] :
( ~ ( SV23 @ SY350 )
| ( SY349 = SY350 ) ) ) )
= $false )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(253,plain,
! [SV59: $i > $o,SV24: $i,SV77: $i] :
( ( ~ ( in @ SV77 @ SV24 )
| ~ ( SV59 @ SV77 )
| ( in @ SV77
@ ( dsetconstr @ SV24
@ ^ [SY434: $i] : ( SV59 @ SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(254,plain,
! [SV25: $i,SV78: $i,SV60: $i] :
( ( ~ ( in @ SV60 @ SV78 )
| ~ ( in @ SV78 @ SV25 )
| ( in @ SV60 @ ( setunion @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(255,plain,
! [SV26: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV26 ) )
= $true )
| ( ( in @ SV61 @ ( powerset @ ( setunion @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(256,plain,
! [SV27: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( setunion @ SV27 ) ) )
= $true )
| ( ( ! [SY436: $o] :
( ~ ! [SY437: $i] :
( ~ ( in @ SV62 @ SY437 )
| ~ ( in @ SY437 @ SV27 )
| SY436 )
| SY436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(257,plain,
! [SV63: $i,SV28: $i] :
( ( ( ~ ( ( SV28 != SV63 ) ) )
= $true )
| ( ( ~ ( in @ SV63 @ ( setadjoin @ SV28 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(258,plain,
! [SV64: $i,SV29: $i,SV79: $i] :
( ( ~ ( in @ SV79 @ ( setadjoin @ SV29 @ SV64 ) )
| ( SV79 = SV29 )
| ( in @ SV79 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(259,plain,
! [SV30: $i] :
( ( ( ~ ! [SY365: $i] :
~ ( in @ SY365 @ SV30 ) )
= $false )
| ( ( ~ ! [SY366: $i] :
~ ~ ( ~ ( in @ SY366 @ SV30 )
| ~ ~ ~ ! [SY367: $i] :
~ ~ ( ~ ( in @ SY367 @ SY366 )
| ~ ( in @ SY367 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(260,plain,
( ( ! [SY456: $i] :
( ~ ( in @ SY456 @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY439 @ emptyset ) ) )
| ( SY456 = sK1_SX0 )
| ( SY456 = sK2_SY439 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[218]) ).
thf(261,plain,
! [SV65: $i > $o,SV31: $i,SV80: $i] :
( ( ~ ( in @ SV80
@ ( dsetconstr @ SV31
@ ^ [SY442: $i] : ( SV65 @ SY442 ) ) )
| ( SV65 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(262,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ~ ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
| ! [SY458: $o] :
( ~ ( ( SV81 != SV32 )
| SY458 )
| ~ ( ~ ( in @ SV81 @ SV66 )
| SY458 )
| SY458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(263,plain,
! [SV33: $i] :
( ( ( SV33 != emptyset )
= $false )
| ( ( ~ ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ SV33 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(264,plain,
! [SV34: $i] :
( ( ( ! [SY375: $i] :
~ ( in @ SY375 @ SV34 ) )
= $false )
| ( ( SV34 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(265,plain,
! [SV35: $i] :
( ( ( ! [SY376: $i] :
~ ( in @ SY376 @ SV35 ) )
= $false )
| ( ( SV35 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(266,plain,
! [SV36: $i] :
( ( ( in @ SV36 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(267,plain,
! [SV67: $i,SV37: $i] :
( ( ( ~ ! [SY445: $i] :
( ~ ( in @ SY445 @ SV37 )
| ( in @ SY445 @ SV67 ) ) )
= $true )
| ( ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) )
| ( SV37 = SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(268,plain,
! [SV68: $i,SV38: $i] :
( ( ( SV38 != SV68 )
= $true )
| ( ( in @ SV38 @ ( setadjoin @ SV68 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(269,plain,
! [SV39: $i,SV69: $i] :
( ( ~ ( ~ ( in @ SV69 @ ( powerset @ SV39 ) )
| ! [SY447: $i] :
( ~ ( in @ SY447 @ SV69 )
| ( in @ SY447 @ SV39 ) ) )
| ~ ( ~ ! [SY448: $i] :
( ~ ( in @ SY448 @ SV69 )
| ( in @ SY448 @ SV39 ) )
| ( in @ SV69 @ ( powerset @ SV39 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(270,plain,
! [SV40: $i,SV70: $i,SV82: $i] :
( ( ~ ( in @ SV82 @ SV70 )
| ( in @ SV82 @ ( setadjoin @ SV40 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(271,plain,
! [SV41: $i > $o] :
( ( ( ~ ! [SY386: $i] :
~ ~ ( ~ ( SV41 @ SY386 )
| ~ ! [SY387: $i] :
( ~ ( SV41 @ SY387 )
| ( SY386 = SY387 ) ) ) )
= $false )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(272,plain,
! [SV71: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ ( setadjoin @ SV71 @ emptyset ) ) )
= $true )
| ( ( SV42 = SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(273,plain,
! [SV43: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) )
| ~ ! [SY464: $i,SY465: $i] :
( ~ ~ ( ~ ( in @ SY464 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY465 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY464 )
| ( in @ SX4 @ SY465 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY465 )
| ( in @ SX4 @ SY464 ) ) ) )
| ~ ! [SY468: $i] :
( ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY468 )
| ( in @ SY401 @ SV43 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY468 ) )
| ~ ! [SY471: $i] :
~ ~ ! [SY472: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY471 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY472 @ SY468 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY471 )
| ~ ( in @ SX5 @ SY468 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY471 ) )
| ( in @ SY472 @ SY474 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[231]) ).
thf(274,plain,
! [SV44: $i] :
( ( ( in @ SV44 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(275,plain,
! [SV83: $i,SV45: $i,SV72: $i] :
( ( ~ ( in @ SV72 @ ( powerset @ SV45 ) )
| ~ ( in @ SV83 @ SV72 )
| ( in @ SV83 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(276,plain,
! [SV47: $i > $o,SV7: $i,SV73: $i] :
( ( ( ~ ( in @ SV73
@ ( dsetconstr @ SV7
@ ^ [SY412: $i] : ( SV47 @ SY412 ) ) ) )
= $true )
| ( ( in @ SV73 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(277,plain,
! [SV8: $i > $o] :
( ( ( ! [SY311: $i] :
~ ~ ( ~ ( SV8 @ SY311 )
| ~ ! [SY312: $i] :
( ~ ( SV8 @ SY312 )
| ( SY311 = SY312 ) ) ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(278,plain,
! [SV9: $o,SV48: $i] :
( ( ( in @ SV48
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY315: $i] : SV9 ) )
= $false )
| ( SV9 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(279,plain,
! [SV49: $i] :
( ( ( in @ SV49
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(280,plain,
! [SV50: $i] :
( ( ( in @ SV50
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(281,plain,
! [SV10: $i] :
( ( ( ~ ( in @ emptyset @ SV10 )
| ~ ! [SY316: $i] :
( ~ ~ ( ~ ( in @ SY316 @ omega )
| ~ ( in @ SY316 @ SV10 ) )
| ( in @ ( setadjoin @ SY316 @ SY316 ) @ SV10 ) ) )
= $true )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(282,plain,
! [SV11: $i,SV51: $i] :
( ( ~ ( ~ ( in @ SV51 @ ( setunion @ SV11 ) )
| ~ ! [SY416: $i] :
~ ~ ( ~ ( in @ SV51 @ SY416 )
| ~ ( in @ SY416 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(283,plain,
! [SV11: $i,SV51: $i] :
( ( ~ ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( in @ SV51 @ SY417 )
| ~ ( in @ SY417 @ SV11 ) )
| ( in @ SV51 @ ( setunion @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(284,plain,
! [SV52: $i,SV13: $i] :
( ( ( ! [SY418: $i] :
~ ( ~ ( ~ ( in @ SY418 @ SV13 )
| ( in @ SY418 @ SV52 ) )
| ~ ( ~ ( in @ SY418 @ SV52 )
| ( in @ SY418 @ SV13 ) ) ) )
= $false )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(285,plain,
! [SV14: $i] :
( ( ( ! [SY323: $i] :
~ ( in @ SY323 @ SV14 ) )
= $true )
| ( ( SV14 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(286,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ~ ( ~ ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
| ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
| ~ ( ~ ( ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
| ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(287,plain,
! [SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY420: $i] :
( ~ ( in @ SY420 @ SV54 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( SV16 @ SY420 @ SY328 )
| ~ ! [SY329: $i] :
( ~ ( SV16 @ SY420 @ SY329 )
| ( SY328 = SY329 ) ) ) ) )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(288,plain,
! [SV55: $i > $o,SV17: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV17 ) )
= $true )
| ( ( ~ ( SV55 @ SV75 )
| ( ( dsetconstr @ SV17
@ ^ [SY428: $i] : ( SV55 @ SY428 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(289,plain,
! [SV18: $i,SV56: $i] :
( ( ( ! [SY429: $i] :
( ~ ( in @ SY429 @ SV56 )
| ( in @ SY429 @ SV18 ) ) )
= $false )
| ( ( in @ SV56 @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(290,plain,
! [SV57: $i,SV19: $i] :
( ( ( in @ SV19 @ ( setadjoin @ SV57 @ emptyset ) )
= $false )
| ( ( in @ SV57 @ ( setadjoin @ SV19 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(291,plain,
! [SV58: $i > $o,SV20: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY431: $i] : ( SV58 @ SY431 ) ) )
| ( SV58 @ SV76 ) )
| ~ ( ~ ( SV58 @ SV76 )
| ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY432: $i] : ( SV58 @ SY432 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(292,plain,
! [SV21: $i] :
( ( ( SV21 = emptyset )
= $true )
| ( ( ~ ! [SY344: $i] :
~ ( in @ SY344 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(293,plain,
! [SV22: $i > $o] :
( ( ( ! [SY345: $i] :
~ ~ ( ~ ( SV22 @ SY345 )
| ~ ! [SY346: $i] :
( ~ ( SV22 @ SY346 )
| ( SY345 = SY346 ) ) ) )
= $true )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(294,plain,
! [SV23: $i > $o] :
( ( ( ! [SY349: $i] :
~ ~ ( ~ ( SV23 @ SY349 )
| ~ ! [SY350: $i] :
( ~ ( SV23 @ SY350 )
| ( SY349 = SY350 ) ) ) )
= $true )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(295,plain,
! [SV59: $i > $o,SV24: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ SV24 ) )
= $true )
| ( ( ~ ( SV59 @ SV77 )
| ( in @ SV77
@ ( dsetconstr @ SV24
@ ^ [SY434: $i] : ( SV59 @ SY434 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(296,plain,
! [SV25: $i,SV78: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ SV78 ) )
= $true )
| ( ( ~ ( in @ SV78 @ SV25 )
| ( in @ SV60 @ ( setunion @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(297,plain,
! [SV26: $i,SV61: $i] :
( ( ( in @ SV61 @ SV26 )
= $false )
| ( ( in @ SV61 @ ( powerset @ ( setunion @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(298,plain,
! [SV27: $i,SV62: $i] :
( ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false )
| ( ( ! [SY436: $o] :
( ~ ! [SY437: $i] :
( ~ ( in @ SV62 @ SY437 )
| ~ ( in @ SY437 @ SV27 )
| SY436 )
| SY436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(299,plain,
! [SV63: $i,SV28: $i] :
( ( ( SV28 != SV63 )
= $false )
| ( ( ~ ( in @ SV63 @ ( setadjoin @ SV28 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(300,plain,
! [SV64: $i,SV29: $i,SV79: $i] :
( ( ( ~ ( in @ SV79 @ ( setadjoin @ SV29 @ SV64 ) ) )
= $true )
| ( ( ( SV79 = SV29 )
| ( in @ SV79 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(301,plain,
! [SV30: $i] :
( ( ( ! [SY365: $i] :
~ ( in @ SY365 @ SV30 ) )
= $true )
| ( ( ~ ! [SY366: $i] :
~ ~ ( ~ ( in @ SY366 @ SV30 )
| ~ ~ ~ ! [SY367: $i] :
~ ~ ( ~ ( in @ SY367 @ SY366 )
| ~ ( in @ SY367 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(302,plain,
( ( ~ ( in @ sK4_SY456 @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY439 @ emptyset ) ) )
| ( sK4_SY456 = sK1_SX0 )
| ( sK4_SY456 = sK2_SY439 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[260]) ).
thf(303,plain,
! [SV65: $i > $o,SV31: $i,SV80: $i] :
( ( ( ~ ( in @ SV80
@ ( dsetconstr @ SV31
@ ^ [SY442: $i] : ( SV65 @ SY442 ) ) ) )
= $true )
| ( ( SV65 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(304,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) ) )
= $true )
| ( ( ! [SY458: $o] :
( ~ ( ( SV81 != SV32 )
| SY458 )
| ~ ( ~ ( in @ SV81 @ SV66 )
| SY458 )
| SY458 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(305,plain,
! [SV33: $i] :
( ( ( SV33 = emptyset )
= $true )
| ( ( ~ ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ SV33 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(306,plain,
! [SV34: $i] :
( ( ( ~ ( in @ ( sK5_SY375 @ SV34 ) @ SV34 ) )
= $false )
| ( ( SV34 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[264]) ).
thf(307,plain,
! [SV35: $i] :
( ( ( ~ ( in @ ( sK6_SY376 @ SV35 ) @ SV35 ) )
= $false )
| ( ( SV35 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[265]) ).
thf(308,plain,
! [SV67: $i,SV37: $i] :
( ( ( ! [SY445: $i] :
( ~ ( in @ SY445 @ SV37 )
| ( in @ SY445 @ SV67 ) ) )
= $false )
| ( ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) )
| ( SV37 = SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(309,plain,
! [SV68: $i,SV38: $i] :
( ( ( SV38 = SV68 )
= $false )
| ( ( in @ SV38 @ ( setadjoin @ SV68 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(310,plain,
! [SV39: $i,SV69: $i] :
( ( ~ ( ~ ( in @ SV69 @ ( powerset @ SV39 ) )
| ! [SY447: $i] :
( ~ ( in @ SY447 @ SV69 )
| ( in @ SY447 @ SV39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(311,plain,
! [SV39: $i,SV69: $i] :
( ( ~ ( ~ ! [SY448: $i] :
( ~ ( in @ SY448 @ SV69 )
| ( in @ SY448 @ SV39 ) )
| ( in @ SV69 @ ( powerset @ SV39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(312,plain,
! [SV40: $i,SV70: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ SV70 ) )
= $true )
| ( ( in @ SV82 @ ( setadjoin @ SV40 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(313,plain,
! [SV41: $i > $o] :
( ( ( ! [SY386: $i] :
~ ~ ( ~ ( SV41 @ SY386 )
| ~ ! [SY387: $i] :
( ~ ( SV41 @ SY387 )
| ( SY386 = SY387 ) ) ) )
= $true )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(314,plain,
! [SV71: $i,SV42: $i] :
( ( ( in @ SV42 @ ( setadjoin @ SV71 @ emptyset ) )
= $false )
| ( ( SV42 = SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(315,plain,
! [SV43: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) )
| ~ ! [SY464: $i,SY465: $i] :
( ~ ~ ( ~ ( in @ SY464 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY465 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY464 )
| ( in @ SX4 @ SY465 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY465 )
| ( in @ SX4 @ SY464 ) ) ) )
| ~ ! [SY468: $i] :
( ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY468 )
| ( in @ SY401 @ SV43 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY468 ) )
| ~ ! [SY471: $i] :
~ ~ ! [SY472: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY471 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY472 @ SY468 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY471 )
| ~ ( in @ SX5 @ SY468 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY471 ) )
| ( in @ SY472 @ SY474 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(316,plain,
! [SV44: $i,SV84: $o] :
( ( SV84 = $true )
| ( ( in @ SV44 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[274]) ).
thf(317,plain,
! [SV44: $i] :
( ( $true = $true )
| ( ( in @ SV44 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[274]) ).
thf(318,plain,
! [SV44: $i] :
( ( $false = $true )
| ( ( in @ SV44 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[274]) ).
thf(319,plain,
! [SV83: $i,SV45: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ ( powerset @ SV45 ) ) )
= $true )
| ( ( ~ ( in @ SV83 @ SV72 )
| ( in @ SV83 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(320,plain,
! [SV47: $i > $o,SV7: $i,SV73: $i] :
( ( ( in @ SV73
@ ( dsetconstr @ SV7
@ ^ [SY412: $i] : ( SV47 @ SY412 ) ) )
= $false )
| ( ( in @ SV73 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(321,plain,
! [SV85: $i,SV8: $i > $o] :
( ( ( ~ ~ ( ~ ( SV8 @ SV85 )
| ~ ! [SY476: $i] :
( ~ ( SV8 @ SY476 )
| ( SV85 = SY476 ) ) ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(322,plain,
! [SV10: $i] :
( ( ( ~ ( in @ emptyset @ SV10 ) )
= $true )
| ( ( ~ ! [SY316: $i] :
( ~ ~ ( ~ ( in @ SY316 @ omega )
| ~ ( in @ SY316 @ SV10 ) )
| ( in @ ( setadjoin @ SY316 @ SY316 ) @ SV10 ) ) )
= $true )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(323,plain,
! [SV11: $i,SV51: $i] :
( ( ~ ( in @ SV51 @ ( setunion @ SV11 ) )
| ~ ! [SY416: $i] :
~ ~ ( ~ ( in @ SV51 @ SY416 )
| ~ ( in @ SY416 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(324,plain,
! [SV11: $i,SV51: $i] :
( ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( in @ SV51 @ SY417 )
| ~ ( in @ SY417 @ SV11 ) )
| ( in @ SV51 @ ( setunion @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(325,plain,
! [SV13: $i,SV52: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 ) )
| ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) ) ) )
= $false )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[284]) ).
thf(326,plain,
! [SV14: $i,SV86: $i] :
( ( ( ~ ( in @ SV86 @ SV14 ) )
= $true )
| ( ( SV14 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(327,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ~ ( ~ ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
| ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(328,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ~ ( ~ ( ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
| ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(329,plain,
! [SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
| ~ ! [SY477: $i] :
~ ~ ( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY477 )
| ~ ! [SY478: $i] :
( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY478 )
| ( SY477 = SY478 ) ) ) )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[287]) ).
thf(330,plain,
! [SV55: $i > $o,SV17: $i,SV75: $i] :
( ( ( in @ SV75 @ SV17 )
= $false )
| ( ( ~ ( SV55 @ SV75 )
| ( ( dsetconstr @ SV17
@ ^ [SY428: $i] : ( SV55 @ SY428 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(331,plain,
! [SV56: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK9_SY429 @ SV18 @ SV56 ) @ SV56 )
| ( in @ ( sK9_SY429 @ SV18 @ SV56 ) @ SV18 ) )
= $false )
| ( ( in @ SV56 @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[289]) ).
thf(332,plain,
! [SV58: $i > $o,SV20: $i,SV76: $i] :
( ( ( in @ SV76 @ SV20 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY431: $i] : ( SV58 @ SY431 ) ) )
| ( SV58 @ SV76 ) )
| ~ ( ~ ( SV58 @ SV76 )
| ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY432: $i] : ( SV58 @ SY432 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(333,plain,
! [SV21: $i] :
( ( ( ! [SY344: $i] :
~ ( in @ SY344 @ SV21 ) )
= $false )
| ( ( SV21 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(334,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ~ ( ~ ( SV22 @ SV87 )
| ~ ! [SY479: $i] :
( ~ ( SV22 @ SY479 )
| ( SV87 = SY479 ) ) ) )
= $true )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(335,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ~ ~ ( ~ ( SV23 @ SV88 )
| ~ ! [SY480: $i] :
( ~ ( SV23 @ SY480 )
| ( SV88 = SY480 ) ) ) )
= $true )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(336,plain,
! [SV59: $i > $o,SV24: $i,SV77: $i] :
( ( ( in @ SV77 @ SV24 )
= $false )
| ( ( ~ ( SV59 @ SV77 )
| ( in @ SV77
@ ( dsetconstr @ SV24
@ ^ [SY434: $i] : ( SV59 @ SY434 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(337,plain,
! [SV25: $i,SV78: $i,SV60: $i] :
( ( ( in @ SV60 @ SV78 )
= $false )
| ( ( ~ ( in @ SV78 @ SV25 )
| ( in @ SV60 @ ( setunion @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(338,plain,
! [SV89: $o,SV27: $i,SV62: $i] :
( ( ( ~ ! [SY481: $i] :
( ~ ( in @ SV62 @ SY481 )
| ~ ( in @ SY481 @ SV27 )
| SV89 )
| SV89 )
= $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[298]) ).
thf(339,plain,
! [SV27: $i,SV62: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $true )
| $true )
= $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[298]) ).
thf(340,plain,
! [SV27: $i,SV62: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $false )
| $false )
= $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[298]) ).
thf(341,plain,
! [SV63: $i,SV28: $i] :
( ( ( SV28 = SV63 )
= $true )
| ( ( ~ ( in @ SV63 @ ( setadjoin @ SV28 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(342,plain,
! [SV64: $i,SV29: $i,SV79: $i] :
( ( ( in @ SV79 @ ( setadjoin @ SV29 @ SV64 ) )
= $false )
| ( ( ( SV79 = SV29 )
| ( in @ SV79 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(343,plain,
! [SV30: $i,SV90: $i] :
( ( ( ~ ( in @ SV90 @ SV30 ) )
= $true )
| ( ( ~ ! [SY366: $i] :
~ ~ ( ~ ( in @ SY366 @ SV30 )
| ~ ~ ~ ! [SY367: $i] :
~ ~ ( ~ ( in @ SY367 @ SY366 )
| ~ ( in @ SY367 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(344,plain,
( ( ~ ( in @ sK4_SY456 @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY439 @ emptyset ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(345,plain,
( ( ( sK4_SY456 = sK1_SX0 )
| ( sK4_SY456 = sK2_SY439 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(346,plain,
! [SV65: $i > $o,SV31: $i,SV80: $i] :
( ( ( in @ SV80
@ ( dsetconstr @ SV31
@ ^ [SY442: $i] : ( SV65 @ SY442 ) ) )
= $false )
| ( ( SV65 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(347,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false )
| ( ( ! [SY458: $o] :
( ~ ( ( SV81 != SV32 )
| SY458 )
| ~ ( ~ ( in @ SV81 @ SV66 )
| SY458 )
| SY458 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(348,plain,
! [SV33: $i] :
( ( ( ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ SV33 )
| ~ $true ) )
= $false )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(349,plain,
! [SV34: $i] :
( ( ( in @ ( sK5_SY375 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(350,plain,
! [SV35: $i] :
( ( ( in @ ( sK6_SY376 @ SV35 ) @ SV35 )
= $true )
| ( ( SV35 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(351,plain,
! [SV37: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV37 )
| ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV67 ) )
= $false )
| ( ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) )
| ( SV37 = SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[308]) ).
thf(352,plain,
! [SV39: $i,SV69: $i] :
( ( ~ ( in @ SV69 @ ( powerset @ SV39 ) )
| ! [SY447: $i] :
( ~ ( in @ SY447 @ SV69 )
| ( in @ SY447 @ SV39 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(353,plain,
! [SV39: $i,SV69: $i] :
( ( ~ ! [SY448: $i] :
( ~ ( in @ SY448 @ SV69 )
| ( in @ SY448 @ SV39 ) )
| ( in @ SV69 @ ( powerset @ SV39 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(354,plain,
! [SV40: $i,SV70: $i,SV82: $i] :
( ( ( in @ SV82 @ SV70 )
= $false )
| ( ( in @ SV82 @ ( setadjoin @ SV40 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(355,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ~ ~ ( ~ ( SV41 @ SV91 )
| ~ ! [SY482: $i] :
( ~ ( SV41 @ SY482 )
| ( SV91 = SY482 ) ) ) )
= $true )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(356,plain,
! [SV43: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) )
| ~ ! [SY464: $i,SY465: $i] :
( ~ ~ ( ~ ( in @ SY464 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY465 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY464 )
| ( in @ SX4 @ SY465 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY465 )
| ( in @ SX4 @ SY464 ) ) ) )
| ~ ! [SY468: $i] :
( ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY468 )
| ( in @ SY401 @ SV43 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY468 ) )
| ~ ! [SY471: $i] :
~ ~ ! [SY472: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY471 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY472 @ SY468 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY471 )
| ~ ( in @ SX5 @ SY468 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY471 ) )
| ( in @ SY472 @ SY474 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(357,plain,
! [SV83: $i,SV45: $i,SV72: $i] :
( ( ( in @ SV72 @ ( powerset @ SV45 ) )
= $false )
| ( ( ~ ( in @ SV83 @ SV72 )
| ( in @ SV83 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(358,plain,
! [SV85: $i,SV8: $i > $o] :
( ( ( ~ ( ~ ( SV8 @ SV85 )
| ~ ! [SY476: $i] :
( ~ ( SV8 @ SY476 )
| ( SV85 = SY476 ) ) ) )
= $false )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(359,plain,
! [SV10: $i] :
( ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ~ ! [SY316: $i] :
( ~ ~ ( ~ ( in @ SY316 @ omega )
| ~ ( in @ SY316 @ SV10 ) )
| ( in @ ( setadjoin @ SY316 @ SY316 ) @ SV10 ) ) )
= $true )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(360,plain,
! [SV11: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( setunion @ SV11 ) ) )
= $true )
| ( ( ~ ! [SY416: $i] :
~ ~ ( ~ ( in @ SV51 @ SY416 )
| ~ ( in @ SY416 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(361,plain,
! [SV11: $i,SV51: $i] :
( ( ( ~ ~ ! [SY417: $i] :
~ ~ ( ~ ( in @ SV51 @ SY417 )
| ~ ( in @ SY417 @ SV11 ) ) )
= $true )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(362,plain,
! [SV13: $i,SV52: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 ) )
| ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(363,plain,
! [SV14: $i,SV86: $i] :
( ( ( in @ SV86 @ SV14 )
= $false )
| ( ( SV14 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(364,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ~ ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
| ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(365,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ~ ( ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
| ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(366,plain,
! [SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 ) )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(367,plain,
! [SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ! [SY477: $i] :
~ ~ ( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY477 )
| ~ ! [SY478: $i] :
( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY478 )
| ( SY477 = SY478 ) ) ) )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(368,plain,
! [SV17: $i,SV75: $i,SV55: $i > $o] :
( ( ( ~ ( SV55 @ SV75 ) )
= $true )
| ( ( ( dsetconstr @ SV17
@ ^ [SY428: $i] : ( SV55 @ SY428 ) )
!= emptyset )
= $true )
| ( ( in @ SV75 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(369,plain,
! [SV56: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK9_SY429 @ SV18 @ SV56 ) @ SV56 ) )
= $false )
| ( ( in @ SV56 @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(370,plain,
! [SV56: $i,SV18: $i] :
( ( ( in @ ( sK9_SY429 @ SV18 @ SV56 ) @ SV18 )
= $false )
| ( ( in @ SV56 @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(371,plain,
! [SV58: $i > $o,SV20: $i,SV76: $i] :
( ( ( ~ ( ~ ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY431: $i] : ( SV58 @ SY431 ) ) )
| ( SV58 @ SV76 ) )
| ~ ( ~ ( SV58 @ SV76 )
| ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY432: $i] : ( SV58 @ SY432 ) ) ) ) )
= $false )
| ( ( in @ SV76 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(372,plain,
! [SV21: $i] :
( ( ( ~ ( in @ ( sK11_SY344 @ SV21 ) @ SV21 ) )
= $false )
| ( ( SV21 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[333]) ).
thf(373,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( ~ ( SV22 @ SV87 )
| ~ ! [SY479: $i] :
( ~ ( SV22 @ SY479 )
| ( SV87 = SY479 ) ) ) )
= $false )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(374,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ~ ( ~ ( SV23 @ SV88 )
| ~ ! [SY480: $i] :
( ~ ( SV23 @ SY480 )
| ( SV88 = SY480 ) ) ) )
= $false )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(375,plain,
! [SV24: $i,SV77: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ SV77 ) )
= $true )
| ( ( in @ SV77
@ ( dsetconstr @ SV24
@ ^ [SY434: $i] : ( SV59 @ SY434 ) ) )
= $true )
| ( ( in @ SV77 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(376,plain,
! [SV60: $i,SV25: $i,SV78: $i] :
( ( ( ~ ( in @ SV78 @ SV25 ) )
= $true )
| ( ( in @ SV60 @ ( setunion @ SV25 ) )
= $true )
| ( ( in @ SV60 @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(377,plain,
! [SV89: $o,SV27: $i,SV62: $i] :
( ( ( ~ ! [SY481: $i] :
( ~ ( in @ SV62 @ SY481 )
| ~ ( in @ SY481 @ SV27 )
| SV89 ) )
= $true )
| ( SV89 = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(378,plain,
! [SV27: $i,SV62: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(379,plain,
! [SV27: $i,SV62: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(380,plain,
! [SV28: $i,SV63: $i] :
( ( ( in @ SV63 @ ( setadjoin @ SV28 @ emptyset ) )
= $false )
| ( ( SV28 = SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(381,plain,
! [SV64: $i,SV29: $i,SV79: $i] :
( ( ( SV79 = SV29 )
= $true )
| ( ( in @ SV79 @ SV64 )
= $true )
| ( ( in @ SV79 @ ( setadjoin @ SV29 @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(382,plain,
! [SV30: $i,SV90: $i] :
( ( ( in @ SV90 @ SV30 )
= $false )
| ( ( ~ ! [SY366: $i] :
~ ~ ( ~ ( in @ SY366 @ SV30 )
| ~ ~ ~ ! [SY367: $i] :
~ ~ ( ~ ( in @ SY367 @ SY366 )
| ~ ( in @ SY367 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(383,plain,
( ( in @ sK4_SY456 @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY439 @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(384,plain,
( ( sK4_SY456 = sK1_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(385,plain,
( ( sK4_SY456 = sK2_SY439 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(386,plain,
! [SV66: $i,SV92: $o,SV32: $i,SV81: $i] :
( ( ( ~ ( ( SV81 != SV32 )
| SV92 )
| ~ ( ~ ( in @ SV81 @ SV66 )
| SV92 )
| SV92 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[347]) ).
thf(387,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( ~ ( ( SV81 != SV32 )
| $true )
| ~ ( ~ ( in @ SV81 @ SV66 )
| $true )
| $true )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[347]) ).
thf(388,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( ~ ( ( SV81 != SV32 )
| $false )
| ~ ( ~ ( in @ SV81 @ SV66 )
| $false )
| $false )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[347]) ).
thf(389,plain,
! [SV33: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_SY374 @ SV33 ) @ SV33 )
| ~ $true ) )
= $false )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[348]) ).
thf(390,plain,
! [SV37: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV37 ) )
= $false )
| ( ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) )
| ( SV37 = SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(391,plain,
! [SV37: $i,SV67: $i] :
( ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV67 )
= $false )
| ( ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) )
| ( SV37 = SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(392,plain,
! [SV39: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ ( powerset @ SV39 ) ) )
= $true )
| ( ( ! [SY447: $i] :
( ~ ( in @ SY447 @ SV69 )
| ( in @ SY447 @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(393,plain,
! [SV39: $i,SV69: $i] :
( ( ( ~ ! [SY448: $i] :
( ~ ( in @ SY448 @ SV69 )
| ( in @ SY448 @ SV39 ) ) )
= $true )
| ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(394,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ~ ( ~ ( SV41 @ SV91 )
| ~ ! [SY482: $i] :
( ~ ( SV41 @ SY482 )
| ( SV91 = SY482 ) ) ) )
= $false )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(395,plain,
! [SV43: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) )
| ~ ! [SY464: $i,SY465: $i] :
( ~ ~ ( ~ ( in @ SY464 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY465 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY464 )
| ( in @ SX4 @ SY465 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY465 )
| ( in @ SX4 @ SY464 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(396,plain,
! [SV43: $i] :
( ( ~ ! [SY468: $i] :
( ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY468 )
| ( in @ SY401 @ SV43 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY468 ) )
| ~ ! [SY471: $i] :
~ ~ ! [SY472: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY471 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY472 @ SY468 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY471 )
| ~ ( in @ SX5 @ SY468 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY471 ) )
| ( in @ SY472 @ SY474 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(397,plain,
! [SV45: $i,SV72: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV72 ) )
= $true )
| ( ( in @ SV83 @ SV45 )
= $true )
| ( ( in @ SV72 @ ( powerset @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(398,plain,
! [SV85: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ SV85 )
| ~ ! [SY476: $i] :
( ~ ( SV8 @ SY476 )
| ( SV85 = SY476 ) ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(399,plain,
! [SV10: $i] :
( ( ( ! [SY316: $i] :
( ~ ~ ( ~ ( in @ SY316 @ omega )
| ~ ( in @ SY316 @ SV10 ) )
| ( in @ ( setadjoin @ SY316 @ SY316 ) @ SV10 ) ) )
= $false )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(400,plain,
! [SV11: $i,SV51: $i] :
( ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $false )
| ( ( ~ ! [SY416: $i] :
~ ~ ( ~ ( in @ SV51 @ SY416 )
| ~ ( in @ SY416 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(401,plain,
! [SV11: $i,SV51: $i] :
( ( ( ~ ! [SY417: $i] :
~ ~ ( ~ ( in @ SV51 @ SY417 )
| ~ ( in @ SY417 @ SV11 ) ) )
= $false )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(402,plain,
! [SV13: $i,SV52: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(403,plain,
! [SV86: $i,SV14: $i] :
( ( ( SV14 = emptyset )
= $false )
| ( ( in @ SV86 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(404,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) ) )
= $true )
| ( ( ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(405,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ( ~ ( ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) ) )
= $true )
| ( ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(406,plain,
! [SV54: $i,SV16: $i > $i > $o] :
( ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(407,plain,
! [SV54: $i,SV16: $i > $i > $o] :
( ( ( ! [SY477: $i] :
~ ~ ( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY477 )
| ~ ! [SY478: $i] :
( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY478 )
| ( SY477 = SY478 ) ) ) )
= $true )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(408,plain,
! [SV17: $i,SV75: $i,SV55: $i > $o] :
( ( ( SV55 @ SV75 )
= $false )
| ( ( ( dsetconstr @ SV17
@ ^ [SY428: $i] : ( SV55 @ SY428 ) )
!= emptyset )
= $true )
| ( ( in @ SV75 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(409,plain,
! [SV56: $i,SV18: $i] :
( ( ( in @ ( sK9_SY429 @ SV18 @ SV56 ) @ SV56 )
= $true )
| ( ( in @ SV56 @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(410,plain,
! [SV58: $i > $o,SV20: $i,SV76: $i] :
( ( ( ~ ( ~ ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY431: $i] : ( SV58 @ SY431 ) ) )
| ( SV58 @ SV76 ) ) )
= $false )
| ( ( in @ SV76 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(411,plain,
! [SV20: $i,SV76: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ SV76 )
| ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY432: $i] : ( SV58 @ SY432 ) ) ) ) )
= $false )
| ( ( in @ SV76 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(412,plain,
! [SV21: $i] :
( ( ( in @ ( sK11_SY344 @ SV21 ) @ SV21 )
= $true )
| ( ( SV21 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(413,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ SV87 )
| ~ ! [SY479: $i] :
( ~ ( SV22 @ SY479 )
| ( SV87 = SY479 ) ) )
= $true )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(414,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ SV88 )
| ~ ! [SY480: $i] :
( ~ ( SV23 @ SY480 )
| ( SV88 = SY480 ) ) )
= $true )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(415,plain,
! [SV24: $i,SV77: $i,SV59: $i > $o] :
( ( ( SV59 @ SV77 )
= $false )
| ( ( in @ SV77
@ ( dsetconstr @ SV24
@ ^ [SY434: $i] : ( SV59 @ SY434 ) ) )
= $true )
| ( ( in @ SV77 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(416,plain,
! [SV60: $i,SV25: $i,SV78: $i] :
( ( ( in @ SV78 @ SV25 )
= $false )
| ( ( in @ SV60 @ ( setunion @ SV25 ) )
= $true )
| ( ( in @ SV60 @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(417,plain,
! [SV89: $o,SV27: $i,SV62: $i] :
( ( ( ! [SY481: $i] :
( ~ ( in @ SV62 @ SY481 )
| ~ ( in @ SY481 @ SV27 )
| SV89 ) )
= $false )
| ( SV89 = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(418,plain,
! [SV27: $i,SV62: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(419,plain,
! [SV27: $i,SV62: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(420,plain,
! [SV90: $i,SV30: $i] :
( ( ( ! [SY366: $i] :
~ ~ ( ~ ( in @ SY366 @ SV30 )
| ~ ~ ~ ! [SY367: $i] :
~ ~ ( ~ ( in @ SY367 @ SY366 )
| ~ ( in @ SY367 @ SV30 ) ) ) )
= $false )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(421,plain,
! [SV66: $i,SV92: $o,SV32: $i,SV81: $i] :
( ( ( ~ ( ( SV81 != SV32 )
| SV92 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| SV92 )
| SV92 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(422,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( ~ ( ( SV81 != SV32 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $true )
| $true )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(423,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( ~ ( ( SV81 != SV32 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $false )
| $false )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(424,plain,
! [SV33: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY374 @ SV33 ) @ SV33 )
| ~ $true ) )
= $true )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(425,plain,
! [SV37: $i,SV67: $i] :
( ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV37 )
= $true )
| ( ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) )
| ( SV37 = SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(426,plain,
! [SV37: $i,SV67: $i] :
( ( ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) ) )
= $true )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(427,plain,
! [SV39: $i,SV69: $i] :
( ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $false )
| ( ( ! [SY447: $i] :
( ~ ( in @ SY447 @ SV69 )
| ( in @ SY447 @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(428,plain,
! [SV39: $i,SV69: $i] :
( ( ( ! [SY448: $i] :
( ~ ( in @ SY448 @ SV69 )
| ( in @ SY448 @ SV39 ) ) )
= $false )
| ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(429,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ SV91 )
| ~ ! [SY482: $i] :
( ~ ( SV41 @ SY482 )
| ( SV91 = SY482 ) ) )
= $true )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(430,plain,
! [SV43: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) )
| ~ ! [SY464: $i,SY465: $i] :
( ~ ~ ( ~ ( in @ SY464 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY465 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY464 )
| ( in @ SX4 @ SY465 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY465 )
| ( in @ SX4 @ SY464 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(431,plain,
! [SV43: $i] :
( ( ! [SY468: $i] :
( ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY468 )
| ( in @ SY401 @ SV43 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY468 ) )
| ~ ! [SY471: $i] :
~ ~ ! [SY472: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY471 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY472 @ SY468 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY471 )
| ~ ( in @ SX5 @ SY468 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY471 ) )
| ( in @ SY472 @ SY474 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(432,plain,
! [SV45: $i,SV72: $i,SV83: $i] :
( ( ( in @ SV83 @ SV72 )
= $false )
| ( ( in @ SV83 @ SV45 )
= $true )
| ( ( in @ SV72 @ ( powerset @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(433,plain,
! [SV85: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ SV85 ) )
= $true )
| ( ( ~ ! [SY476: $i] :
( ~ ( SV8 @ SY476 )
| ( SV85 = SY476 ) ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(434,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY316 @ SV10 ) @ omega )
| ~ ( in @ ( sK13_SY316 @ SV10 ) @ SV10 ) )
| ( in @ ( setadjoin @ ( sK13_SY316 @ SV10 ) @ ( sK13_SY316 @ SV10 ) ) @ SV10 ) )
= $false )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[399]) ).
thf(435,plain,
! [SV11: $i,SV51: $i] :
( ( ( ! [SY416: $i] :
~ ~ ( ~ ( in @ SV51 @ SY416 )
| ~ ( in @ SY416 @ SV11 ) ) )
= $false )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(436,plain,
! [SV11: $i,SV51: $i] :
( ( ( ! [SY417: $i] :
~ ~ ( ~ ( in @ SV51 @ SY417 )
| ~ ( in @ SY417 @ SV11 ) ) )
= $true )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(437,plain,
! [SV13: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(438,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
= $false )
| ( ( ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(439,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ( ( SV74 = SV15 )
| ( in @ SV74 @ SV53 ) )
= $false )
| ( ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(440,plain,
! [SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(441,plain,
! [SV93: $i,SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
| ~ ! [SY483: $i] :
( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY483 )
| ( SV93 = SY483 ) ) ) )
= $true )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(442,plain,
! [SV75: $i,SV55: $i > $o,SV17: $i] :
( ( ( ( dsetconstr @ SV17
@ ^ [SY428: $i] : ( SV55 @ SY428 ) )
= emptyset )
= $false )
| ( ( SV55 @ SV75 )
= $false )
| ( ( in @ SV75 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(443,plain,
! [SV58: $i > $o,SV20: $i,SV76: $i] :
( ( ( ~ ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY431: $i] : ( SV58 @ SY431 ) ) )
| ( SV58 @ SV76 ) )
= $true )
| ( ( in @ SV76 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(444,plain,
! [SV20: $i,SV76: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV76 )
| ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY432: $i] : ( SV58 @ SY432 ) ) ) )
= $true )
| ( ( in @ SV76 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(445,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ SV87 ) )
= $true )
| ( ( ~ ! [SY479: $i] :
( ~ ( SV22 @ SY479 )
| ( SV87 = SY479 ) ) )
= $true )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(446,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ SV88 ) )
= $true )
| ( ( ~ ! [SY480: $i] :
( ~ ( SV23 @ SY480 )
| ( SV88 = SY480 ) ) )
= $true )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(447,plain,
! [SV27: $i,SV89: $o,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK14_SY481 @ SV89 @ SV27 @ SV62 ) )
| ~ ( in @ ( sK14_SY481 @ SV89 @ SV27 @ SV62 ) @ SV27 )
| SV89 )
= $false )
| ( SV89 = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[417]) ).
thf(448,plain,
! [SV27: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK15_SX0 @ SV27 @ SV62 ) )
| ~ ( in @ ( sK15_SX0 @ SV27 @ SV62 ) @ SV27 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[418]) ).
thf(449,plain,
! [SV27: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK16_SX0 @ SV27 @ SV62 ) )
| ~ ( in @ ( sK16_SX0 @ SV27 @ SV62 ) @ SV27 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[419]) ).
thf(450,plain,
! [SV30: $i,SV90: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY366 @ SV90 @ SV30 ) @ SV30 )
| ~ ~ ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SY484 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SY484 @ SV30 ) ) ) )
= $false )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[420]) ).
thf(451,plain,
! [SV66: $i,SV92: $o,SV32: $i,SV81: $i] :
( ( ( ( SV81 != SV32 )
| SV92 )
= $false )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| SV92 )
| SV92 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(452,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( ( SV81 != SV32 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $true )
| $true )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(453,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( ( SV81 != SV32 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $false )
| $false )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(454,plain,
! [SV33: $i] :
( ( ( ~ ( in @ ( sK12_SY374 @ SV33 ) @ SV33 )
| ~ $true )
= $false )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(455,plain,
! [SV37: $i,SV67: $i] :
( ( ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) ) )
= $true )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(456,plain,
! [SV37: $i,SV67: $i] :
( ( ( ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) ) )
= $false )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(457,plain,
! [SV39: $i,SV69: $i,SV94: $i] :
( ( ( ~ ( in @ SV94 @ SV69 )
| ( in @ SV94 @ SV39 ) )
= $true )
| ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(458,plain,
! [SV69: $i,SV39: $i] :
( ( ( ~ ( in @ ( sK18_SY448 @ SV39 @ SV69 ) @ SV69 )
| ( in @ ( sK18_SY448 @ SV39 @ SV69 ) @ SV39 ) )
= $false )
| ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[428]) ).
thf(459,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ SV91 ) )
= $true )
| ( ( ~ ! [SY482: $i] :
( ~ ( SV41 @ SY482 )
| ( SV91 = SY482 ) ) )
= $true )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(460,plain,
! [SV43: $i] :
( ( ~ ~ ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) )
| ~ ! [SY464: $i,SY465: $i] :
( ~ ~ ( ~ ( in @ SY464 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY465 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY464 )
| ( in @ SX4 @ SY465 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY465 )
| ( in @ SX4 @ SY464 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(461,plain,
! [SV43: $i,SV95: $i] :
( ( ~ ~ ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SV95 )
| ( in @ SY485 @ SV43 ) )
| ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
| ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(462,plain,
! [SV85: $i,SV8: $i > $o] :
( ( ( SV8 @ SV85 )
= $false )
| ( ( ~ ! [SY476: $i] :
( ~ ( SV8 @ SY476 )
| ( SV85 = SY476 ) ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(463,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY316 @ SV10 ) @ omega )
| ~ ( in @ ( sK13_SY316 @ SV10 ) @ SV10 ) ) )
= $false )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(464,plain,
! [SV10: $i] :
( ( ( in @ ( setadjoin @ ( sK13_SY316 @ SV10 ) @ ( sK13_SY316 @ SV10 ) ) @ SV10 )
= $false )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(465,plain,
! [SV11: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( in @ SV51 @ ( sK19_SY416 @ SV11 @ SV51 ) )
| ~ ( in @ ( sK19_SY416 @ SV11 @ SV51 ) @ SV11 ) ) )
= $false )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[435]) ).
thf(466,plain,
! [SV11: $i,SV96: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( in @ SV51 @ SV96 )
| ~ ( in @ SV96 @ SV11 ) ) )
= $true )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(467,plain,
! [SV13: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(468,plain,
! [SV13: $i,SV52: $i] :
( ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(469,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ( SV74 = SV15 )
= $true )
| ( ( in @ SV74 @ SV53 )
= $true )
| ( ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(470,plain,
! [SV53: $i,SV15: $i,SV74: $i] :
( ( ( SV74 = SV15 )
= $false )
| ( ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(471,plain,
! [SV15: $i,SV53: $i,SV74: $i] :
( ( ( in @ SV74 @ SV53 )
= $false )
| ( ( in @ SV74 @ ( setadjoin @ SV15 @ SV53 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(472,plain,
! [SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ! [SY492: $i] :
~ ( ~ ( ~ ( in @ SY492 @ ( sK20_SY423 @ SV16 @ SV54 ) )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY492 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY492 ) )
| ( in @ SY492 @ ( sK20_SY423 @ SV16 @ SV54 ) ) ) ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[440]) ).
thf(473,plain,
! [SV93: $i,SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
| ~ ! [SY483: $i] :
( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY483 )
| ( SV93 = SY483 ) ) ) )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(474,plain,
! [SV58: $i > $o,SV20: $i,SV76: $i] :
( ( ( ~ ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY431: $i] : ( SV58 @ SY431 ) ) ) )
= $true )
| ( ( SV58 @ SV76 )
= $true )
| ( ( in @ SV76 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(475,plain,
! [SV20: $i,SV76: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV76 ) )
= $true )
| ( ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY432: $i] : ( SV58 @ SY432 ) ) )
= $true )
| ( ( in @ SV76 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(476,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( SV22 @ SV87 )
= $false )
| ( ( ~ ! [SY479: $i] :
( ~ ( SV22 @ SY479 )
| ( SV87 = SY479 ) ) )
= $true )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(477,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( SV23 @ SV88 )
= $false )
| ( ( ~ ! [SY480: $i] :
( ~ ( SV23 @ SY480 )
| ( SV88 = SY480 ) ) )
= $true )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(478,plain,
! [SV27: $i,SV89: $o,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK14_SY481 @ SV89 @ SV27 @ SV62 ) ) )
= $false )
| ( SV89 = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(479,plain,
! [SV62: $i,SV27: $i,SV89: $o] :
( ( ( ~ ( in @ ( sK14_SY481 @ SV89 @ SV27 @ SV62 ) @ SV27 )
| SV89 )
= $false )
| ( SV89 = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(480,plain,
! [SV27: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK15_SX0 @ SV27 @ SV62 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(481,plain,
! [SV62: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK15_SX0 @ SV27 @ SV62 ) @ SV27 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(482,plain,
! [SV27: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK16_SX0 @ SV27 @ SV62 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(483,plain,
! [SV62: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK16_SX0 @ SV27 @ SV62 ) @ SV27 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(484,plain,
! [SV30: $i,SV90: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY366 @ SV90 @ SV30 ) @ SV30 )
| ~ ~ ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SY484 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SY484 @ SV30 ) ) ) )
= $true )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(485,plain,
! [SV92: $o,SV66: $i,SV32: $i,SV81: $i] :
( ( ( SV81 != SV32 )
= $false )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| SV92 )
| SV92 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(486,plain,
! [SV32: $i,SV66: $i,SV81: $i,SV92: $o] :
( ( SV92 = $false )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| SV92 )
| SV92 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(487,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( SV81 != SV32 )
= $false )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $true )
| $true )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(488,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $true )
| $true )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(489,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( SV81 != SV32 )
= $false )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $false )
| $false )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(490,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $false )
| $false )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(491,plain,
! [SV33: $i] :
( ( ( ~ ( in @ ( sK12_SY374 @ SV33 ) @ SV33 ) )
= $false )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(492,plain,
! [SV33: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(493,plain,
! [SV37: $i,SV67: $i] :
( ( ( ! [SY446: $i] :
( ~ ( in @ SY446 @ SV67 )
| ( in @ SY446 @ SV37 ) ) )
= $false )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(494,plain,
! [SV67: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK21_SY446 @ SV37 @ SV67 ) @ SV67 )
| ( in @ ( sK21_SY446 @ SV37 @ SV67 ) @ SV37 ) )
= $false )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV67 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[456]) ).
thf(495,plain,
! [SV39: $i,SV69: $i,SV94: $i] :
( ( ( ~ ( in @ SV94 @ SV69 ) )
= $true )
| ( ( in @ SV94 @ SV39 )
= $true )
| ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(496,plain,
! [SV69: $i,SV39: $i] :
( ( ( ~ ( in @ ( sK18_SY448 @ SV39 @ SV69 ) @ SV69 ) )
= $false )
| ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(497,plain,
! [SV69: $i,SV39: $i] :
( ( ( in @ ( sK18_SY448 @ SV39 @ SV69 ) @ SV39 )
= $false )
| ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(498,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( SV41 @ SV91 )
= $false )
| ( ( ~ ! [SY482: $i] :
( ~ ( SV41 @ SY482 )
| ( SV91 = SY482 ) ) )
= $true )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(499,plain,
! [SV43: $i] :
( ( ~ ~ ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(500,plain,
! [SV43: $i] :
( ( ~ ! [SY464: $i,SY465: $i] :
( ~ ~ ( ~ ( in @ SY464 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY465 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY464 )
| ( in @ SX4 @ SY465 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY465 )
| ( in @ SX4 @ SY464 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(501,plain,
! [SV43: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SV95 )
| ( in @ SY485 @ SV43 ) )
| ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) ) )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(502,plain,
! [SV85: $i,SV8: $i > $o] :
( ( ( ! [SY476: $i] :
( ~ ( SV8 @ SY476 )
| ( SV85 = SY476 ) ) )
= $false )
| ( ( SV8 @ SV85 )
= $false )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(503,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY316 @ SV10 ) @ omega )
| ~ ( in @ ( sK13_SY316 @ SV10 ) @ SV10 ) ) )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(504,plain,
! [SV10: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ omega )
| ( in @ SV97 @ SV10 ) )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( in @ ( setadjoin @ ( sK13_SY316 @ SV10 ) @ ( sK13_SY316 @ SV10 ) ) @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(505,plain,
! [SV11: $i,SV51: $i] :
( ( ( ~ ( ~ ( in @ SV51 @ ( sK19_SY416 @ SV11 @ SV51 ) )
| ~ ( in @ ( sK19_SY416 @ SV11 @ SV51 ) @ SV11 ) ) )
= $true )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(506,plain,
! [SV11: $i,SV96: $i,SV51: $i] :
( ( ( ~ ( ~ ( in @ SV51 @ SV96 )
| ~ ( in @ SV96 @ SV11 ) ) )
= $false )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(507,plain,
! [SV13: $i,SV52: $i] :
( ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(508,plain,
! [SV13: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
= $false )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(509,plain,
! [SV54: $i,SV16: $i > $i > $o] :
( ( ( ! [SY492: $i] :
~ ( ~ ( ~ ( in @ SY492 @ ( sK20_SY423 @ SV16 @ SV54 ) )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY492 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY492 ) )
| ( in @ SY492 @ ( sK20_SY423 @ SV16 @ SV54 ) ) ) ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(510,plain,
! [SV93: $i,SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
| ~ ! [SY483: $i] :
( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY483 )
| ( SV93 = SY483 ) ) )
= $true )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(511,plain,
! [SV58: $i > $o,SV20: $i,SV76: $i] :
( ( ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY431: $i] : ( SV58 @ SY431 ) ) )
= $false )
| ( ( SV58 @ SV76 )
= $true )
| ( ( in @ SV76 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(512,plain,
! [SV20: $i,SV76: $i,SV58: $i > $o] :
( ( ( SV58 @ SV76 )
= $false )
| ( ( in @ SV76
@ ( dsetconstr @ SV20
@ ^ [SY432: $i] : ( SV58 @ SY432 ) ) )
= $true )
| ( ( in @ SV76 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(513,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ! [SY479: $i] :
( ~ ( SV22 @ SY479 )
| ( SV87 = SY479 ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(514,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ! [SY480: $i] :
( ~ ( SV23 @ SY480 )
| ( SV88 = SY480 ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(515,plain,
! [SV27: $i,SV89: $o,SV62: $i] :
( ( ( in @ SV62 @ ( sK14_SY481 @ SV89 @ SV27 @ SV62 ) )
= $true )
| ( SV89 = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(516,plain,
! [SV62: $i,SV27: $i,SV89: $o] :
( ( ( ~ ( in @ ( sK14_SY481 @ SV89 @ SV27 @ SV62 ) @ SV27 ) )
= $false )
| ( SV89 = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(517,plain,
! [SV27: $i,SV62: $i,SV89: $o] :
( ( SV89 = $false )
| ( SV89 = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(518,plain,
! [SV27: $i,SV62: $i] :
( ( ( in @ SV62 @ ( sK15_SX0 @ SV27 @ SV62 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(519,plain,
! [SV62: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK15_SX0 @ SV27 @ SV62 ) @ SV27 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(520,plain,
! [SV27: $i,SV62: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(521,plain,
! [SV27: $i,SV62: $i] :
( ( ( in @ SV62 @ ( sK16_SX0 @ SV27 @ SV62 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(522,plain,
! [SV62: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK16_SX0 @ SV27 @ SV62 ) @ SV27 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(523,plain,
! [SV27: $i,SV62: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(524,plain,
! [SV30: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK17_SY366 @ SV90 @ SV30 ) @ SV30 )
| ~ ~ ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SY484 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SY484 @ SV30 ) ) )
= $false )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(525,plain,
! [SV92: $o,SV66: $i,SV32: $i,SV81: $i] :
( ( ( SV81 = SV32 )
= $true )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| SV92 )
| SV92 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(526,plain,
! [SV32: $i,SV92: $o,SV66: $i,SV81: $i] :
( ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| SV92 ) )
= $true )
| ( SV92 = $true )
| ( SV92 = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(527,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( SV81 = SV32 )
= $true )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $true )
| $true )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(528,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(529,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( ( SV81 = SV32 )
= $true )
| ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $false )
| $false )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(530,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(531,plain,
! [SV33: $i] :
( ( ( in @ ( sK12_SY374 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(532,plain,
! [SV33: $i] :
( ( $true = $true )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(533,plain,
! [SV67: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK22_SY446 @ SV37 @ SV67 ) @ SV67 )
| ( in @ ( sK22_SY446 @ SV37 @ SV67 ) @ SV37 ) )
= $false )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV37 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[493]) ).
thf(534,plain,
! [SV67: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK21_SY446 @ SV37 @ SV67 ) @ SV67 ) )
= $false )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(535,plain,
! [SV67: $i,SV37: $i] :
( ( ( in @ ( sK21_SY446 @ SV37 @ SV67 ) @ SV37 )
= $false )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(536,plain,
! [SV39: $i,SV69: $i,SV94: $i] :
( ( ( in @ SV94 @ SV69 )
= $false )
| ( ( in @ SV94 @ SV39 )
= $true )
| ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(537,plain,
! [SV69: $i,SV39: $i] :
( ( ( in @ ( sK18_SY448 @ SV39 @ SV69 ) @ SV69 )
= $true )
| ( ( in @ SV69 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(538,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ! [SY482: $i] :
( ~ ( SV41 @ SY482 )
| ( SV91 = SY482 ) ) )
= $false )
| ( ( SV41 @ SV91 )
= $false )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(539,plain,
! [SV43: $i] :
( ( ~ ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(540,plain,
! [SV43: $i] :
( ( ! [SY464: $i,SY465: $i] :
( ~ ~ ( ~ ( in @ SY464 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY465 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY464 )
| ( in @ SX4 @ SY465 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY465 )
| ( in @ SX4 @ SY464 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(541,plain,
! [SV43: $i,SV95: $i] :
( ( ( ~ ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SV95 )
| ( in @ SY485 @ SV43 ) )
| ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) ) )
= $false )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(542,plain,
! [SV85: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ ( sK23_SY476 @ SV85 @ SV8 ) )
| ( SV85
= ( sK23_SY476 @ SV85 @ SV8 ) ) )
= $false )
| ( ( SV8 @ SV85 )
= $false )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[502]) ).
thf(543,plain,
! [SV10: $i] :
( ( ( ~ ( in @ ( sK13_SY316 @ SV10 ) @ omega )
| ~ ( in @ ( sK13_SY316 @ SV10 ) @ SV10 ) )
= $false )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(544,plain,
! [SV10: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ omega ) )
= $true )
| ( ( in @ SV97 @ SV10 )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( in @ ( setadjoin @ ( sK13_SY316 @ SV10 ) @ ( sK13_SY316 @ SV10 ) ) @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(545,plain,
! [SV11: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( sK19_SY416 @ SV11 @ SV51 ) )
| ~ ( in @ ( sK19_SY416 @ SV11 @ SV51 ) @ SV11 ) )
= $false )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(546,plain,
! [SV11: $i,SV96: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ SV96 )
| ~ ( in @ SV96 @ SV11 ) )
= $true )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(547,plain,
! [SV13: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
| ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(548,plain,
! [SV13: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 ) )
= $false )
| ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
= $false )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(549,plain,
! [SV13: $i,SV52: $i] :
( ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
= $false )
| ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
= $false )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(550,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
| ~ ! [SY495: $i] :
~ ~ ( ~ ( in @ SY495 @ SV54 )
| ~ ( SV16 @ SY495 @ SV98 ) ) )
| ~ ( ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( in @ SY496 @ SV54 )
| ~ ( SV16 @ SY496 @ SV98 ) )
| ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) ) ) ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(551,plain,
! [SV93: $i,SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 ) )
= $true )
| ( ( ~ ! [SY483: $i] :
( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY483 )
| ( SV93 = SY483 ) ) )
= $true )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(552,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
| ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[513]) ).
thf(553,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
| ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[514]) ).
thf(554,plain,
! [SV62: $i,SV27: $i,SV89: $o] :
( ( ( in @ ( sK14_SY481 @ SV89 @ SV27 @ SV62 ) @ SV27 )
= $true )
| ( SV89 = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(555,plain,
! [SV62: $i,SV27: $i] :
( ( ( in @ ( sK15_SX0 @ SV27 @ SV62 ) @ SV27 )
= $true )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(556,plain,
! [SV62: $i,SV27: $i] :
( ( ( in @ ( sK16_SX0 @ SV27 @ SV62 ) @ SV27 )
= $true )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(557,plain,
! [SV30: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK17_SY366 @ SV90 @ SV30 ) @ SV30 ) )
= $false )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(558,plain,
! [SV30: $i,SV90: $i] :
( ( ( ~ ~ ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SY484 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SY484 @ SV30 ) ) )
= $false )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(559,plain,
! [SV32: $i,SV92: $o,SV66: $i,SV81: $i] :
( ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| SV92 ) )
= $true )
| ( SV92 = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(560,plain,
! [SV32: $i,SV92: $o,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 )
| SV92 )
= $false )
| ( SV92 = $true )
| ( SV92 = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(561,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(562,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(563,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( ~ ( in @ SV81 @ SV66 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(564,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(565,plain,
! [SV67: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK22_SY446 @ SV37 @ SV67 ) @ SV67 ) )
= $false )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(566,plain,
! [SV67: $i,SV37: $i] :
( ( ( in @ ( sK22_SY446 @ SV37 @ SV67 ) @ SV37 )
= $false )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(567,plain,
! [SV67: $i,SV37: $i] :
( ( ( in @ ( sK21_SY446 @ SV37 @ SV67 ) @ SV67 )
= $true )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(568,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ ( sK26_SY482 @ SV91 @ SV41 ) )
| ( SV91
= ( sK26_SY482 @ SV91 @ SV41 ) ) )
= $false )
| ( ( SV41 @ SV91 )
= $false )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[538]) ).
thf(569,plain,
! [SV43: $i] :
( ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(570,plain,
! [SV43: $i,SV99: $i] :
( ( ! [SY497: $i] :
( ~ ~ ( ~ ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY497 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SY498: $i] :
( ~ ( in @ SY498 @ SV99 )
| ( in @ SY498 @ SY497 ) )
| ! [SY499: $i] :
( ~ ( in @ SY499 @ SY497 )
| ( in @ SY499 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(571,plain,
! [SV43: $i,SV95: $i] :
( ( ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SV95 )
| ( in @ SY485 @ SV43 ) )
| ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(572,plain,
! [SV85: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ ( sK23_SY476 @ SV85 @ SV8 ) ) )
= $false )
| ( ( SV8 @ SV85 )
= $false )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(573,plain,
! [SV8: $i > $o,SV85: $i] :
( ( ( SV85
= ( sK23_SY476 @ SV85 @ SV8 ) )
= $false )
| ( ( SV8 @ SV85 )
= $false )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(574,plain,
! [SV10: $i] :
( ( ( ~ ( in @ ( sK13_SY316 @ SV10 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(575,plain,
! [SV10: $i] :
( ( ( ~ ( in @ ( sK13_SY316 @ SV10 ) @ SV10 ) )
= $false )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(576,plain,
! [SV10: $i,SV97: $i] :
( ( ( in @ SV97 @ omega )
= $false )
| ( ( in @ SV97 @ SV10 )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( in @ ( setadjoin @ ( sK13_SY316 @ SV10 ) @ ( sK13_SY316 @ SV10 ) ) @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(577,plain,
! [SV11: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( sK19_SY416 @ SV11 @ SV51 ) ) )
= $false )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(578,plain,
! [SV51: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK19_SY416 @ SV11 @ SV51 ) @ SV11 ) )
= $false )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(579,plain,
! [SV11: $i,SV96: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ SV96 ) )
= $true )
| ( ( ~ ( in @ SV96 @ SV11 ) )
= $true )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(580,plain,
! [SV13: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 ) )
= $false )
| ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(581,plain,
! [SV13: $i,SV52: $i] :
( ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
= $false )
| ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(582,plain,
! [SV13: $i,SV52: $i] :
( ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
= $true )
| ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
= $false )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(583,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( ~ ( ~ ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
| ~ ! [SY495: $i] :
~ ~ ( ~ ( in @ SY495 @ SV54 )
| ~ ( SV16 @ SY495 @ SV98 ) ) )
| ~ ( ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( in @ SY496 @ SV54 )
| ~ ( SV16 @ SY496 @ SV98 ) )
| ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(584,plain,
! [SV93: $i,SV54: $i,SV16: $i > $i > $o] :
( ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( ~ ! [SY483: $i] :
( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY483 )
| ( SV93 = SY483 ) ) )
= $true )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(585,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(586,plain,
! [SV22: $i > $o,SV87: $i] :
( ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(587,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(588,plain,
! [SV23: $i > $o,SV88: $i] :
( ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(589,plain,
! [SV30: $i,SV90: $i] :
( ( ( in @ ( sK17_SY366 @ SV90 @ SV30 ) @ SV30 )
= $true )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(590,plain,
! [SV30: $i,SV90: $i] :
( ( ( ~ ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SY484 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SY484 @ SV30 ) ) )
= $true )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(591,plain,
! [SV32: $i,SV92: $o,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 )
| SV92 )
= $false )
| ( SV92 = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(592,plain,
! [SV32: $i,SV92: $o,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 ) )
= $false )
| ( SV92 = $true )
| ( SV92 = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(593,plain,
! [SV66: $i,SV32: $i,SV81: $i,SV92: $o] :
( ( SV92 = $false )
| ( SV92 = $true )
| ( SV92 = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(594,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(595,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(596,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(597,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(598,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(599,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(600,plain,
! [SV67: $i,SV37: $i] :
( ( ( in @ ( sK22_SY446 @ SV37 @ SV67 ) @ SV67 )
= $true )
| ( ( SV37 = SV67 )
= $true )
| ( ( in @ ( sK10_SY445 @ SV67 @ SV37 ) @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(601,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ ( sK26_SY482 @ SV91 @ SV41 ) ) )
= $false )
| ( ( SV41 @ SV91 )
= $false )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(602,plain,
! [SV41: $i > $o,SV91: $i] :
( ( ( SV91
= ( sK26_SY482 @ SV91 @ SV41 ) )
= $false )
| ( ( SV41 @ SV91 )
= $false )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(603,plain,
! [SV43: $i] :
( ( ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(604,plain,
! [SV43: $i] :
( ( ~ ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(605,plain,
! [SV100: $i,SV43: $i,SV99: $i] :
( ( ~ ~ ( ~ ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SV100 @ ( sK3_SY390 @ SV43 ) ) )
| ! [SY500: $i] :
( ~ ( in @ SY500 @ SV99 )
| ( in @ SY500 @ SV100 ) )
| ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(606,plain,
! [SV43: $i,SV95: $i] :
( ( ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SV95 )
| ( in @ SY485 @ SV43 ) ) )
= $true )
| ( ( ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(607,plain,
! [SV85: $i,SV8: $i > $o] :
( ( ( SV8 @ ( sK23_SY476 @ SV85 @ SV8 ) )
= $true )
| ( ( SV8 @ SV85 )
= $false )
| ( ( SV8
@ ( descr
@ ^ [SY313: $i] : ( SV8 @ SY313 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(608,plain,
! [SV10: $i] :
( ( ( in @ ( sK13_SY316 @ SV10 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(609,plain,
! [SV10: $i] :
( ( ( in @ ( sK13_SY316 @ SV10 ) @ SV10 )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ omega )
| ( in @ SY317 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(610,plain,
! [SV11: $i,SV51: $i] :
( ( ( in @ SV51 @ ( sK19_SY416 @ SV11 @ SV51 ) )
= $true )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(611,plain,
! [SV51: $i,SV11: $i] :
( ( ( in @ ( sK19_SY416 @ SV11 @ SV51 ) @ SV11 )
= $true )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(612,plain,
! [SV11: $i,SV96: $i,SV51: $i] :
( ( ( in @ SV51 @ SV96 )
= $false )
| ( ( ~ ( in @ SV96 @ SV11 ) )
= $true )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(613,plain,
! [SV13: $i,SV52: $i] :
( ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV52 )
= $true )
| ( ( in @ ( sK7_SY418 @ SV52 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(614,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( ~ ( ~ ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
| ~ ! [SY495: $i] :
~ ~ ( ~ ( in @ SY495 @ SV54 )
| ~ ( SV16 @ SY495 @ SV98 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(615,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ( ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( in @ SY496 @ SV54 )
| ~ ( SV16 @ SY496 @ SV98 ) )
| ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(616,plain,
! [SV93: $i,SV54: $i,SV16: $i > $i > $o] :
( ( ( ! [SY483: $i] :
( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SY483 )
| ( SV93 = SY483 ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(617,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( ~ ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(618,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(619,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( ~ ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(620,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(621,plain,
! [SV30: $i,SV90: $i] :
( ( ( ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SY484 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SY484 @ SV30 ) ) )
= $false )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(622,plain,
! [SV32: $i,SV92: $o,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 ) )
= $false )
| ( SV92 = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(623,plain,
! [SV66: $i,SV32: $i,SV81: $i,SV92: $o] :
( ( SV92 = $false )
| ( SV92 = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(624,plain,
! [SV32: $i,SV92: $o,SV66: $i,SV81: $i] :
( ( ( in @ SV81 @ SV66 )
= $true )
| ( SV92 = $true )
| ( SV92 = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(625,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 ) )
= $false )
| ( $true = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(626,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(627,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( in @ SV81 @ SV66 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(628,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV66 ) )
= $false )
| ( $false = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(629,plain,
! [SV66: $i,SV32: $i,SV81: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(630,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( in @ SV81 @ SV66 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(631,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( SV41 @ ( sK26_SY482 @ SV91 @ SV41 ) )
= $true )
| ( ( SV41 @ SV91 )
= $false )
| ( ( ~ ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(632,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $false )
| ( ( SV41 @ SV91 )
= $false )
| ( ( SV91
= ( sK26_SY482 @ SV91 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(633,plain,
! [SV43: $i] :
( ( ! [SY459: $i] :
( ~ ( in @ SY459 @ ( sK3_SY390 @ SV43 ) )
| ! [SY392: $i] :
( ~ ( in @ SY392 @ SY459 )
| ( in @ SY392 @ SV43 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(634,plain,
! [SV43: $i] :
( ( ! [SY461: $i,SY462: $i] :
( ~ ~ ( ~ ( in @ SY461 @ SV43 )
| ~ ( in @ SY462 @ SV43 ) )
| ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SY461 @ SY463 )
| ( in @ SY462 @ SY463 ) )
| ~ ( ~ ( in @ SY462 @ SY463 )
| ( in @ SY461 @ SY463 ) ) ) )
| ( SY461 = SY462 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(635,plain,
! [SV100: $i,SV43: $i,SV99: $i] :
( ( ( ~ ~ ( ~ ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SV100 @ ( sK3_SY390 @ SV43 ) ) ) )
= $true )
| ( ( ! [SY500: $i] :
( ~ ( in @ SY500 @ SV99 )
| ( in @ SY500 @ SV100 ) )
| ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(636,plain,
! [SV43: $i,SV95: $i] :
( ( ( ! [SY485: $i] :
( ~ ( in @ SY485 @ SV95 )
| ( in @ SY485 @ SV43 ) ) )
= $false )
| ( ( ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(637,plain,
! [SV10: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ omega )
| ( in @ SV101 @ SV10 ) )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( in @ ( sK13_SY316 @ SV10 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(638,plain,
! [SV10: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ omega )
| ( in @ SV102 @ SV10 ) )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( in @ ( sK13_SY316 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(639,plain,
! [SV51: $i,SV11: $i,SV96: $i] :
( ( ( in @ SV96 @ SV11 )
= $false )
| ( ( in @ SV51 @ SV96 )
= $false )
| ( ( in @ SV51 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(640,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( ~ ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
| ~ ! [SY495: $i] :
~ ~ ( ~ ( in @ SY495 @ SV54 )
| ~ ( SV16 @ SY495 @ SV98 ) ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(641,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( in @ SY496 @ SV54 )
| ~ ( SV16 @ SY496 @ SV98 ) )
| ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(642,plain,
! [SV93: $i,SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
| ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[616]) ).
thf(643,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ! [SY347: $i] :
~ ~ ( ~ ( SV22 @ SY347 )
| ~ ! [SY348: $i] :
( ~ ( SV22 @ SY348 )
| ( SY347 = SY348 ) ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(644,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ~ ( ~ ( SV22 @ ( sK28_SY347 @ SV87 @ SV22 ) )
| ~ ! [SY502: $i] :
( ~ ( SV22 @ SY502 )
| ( ( sK28_SY347 @ SV87 @ SV22 )
= SY502 ) ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[618]) ).
thf(645,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ! [SY351: $i] :
~ ! [SY352: $i] :
~ ( ~ ( ~ ( SV23 @ SY352 )
| ( SY352 = SY351 ) )
| ~ ( ( SY352 != SY351 )
| ( SV23 @ SY352 ) ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(646,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ~ ! [SY503: $i] :
~ ( ~ ( ~ ( SV23 @ SY503 )
| ( SY503
= ( sK29_SY351 @ SV88 @ SV23 ) ) )
| ~ ( ( SY503
!= ( sK29_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SY503 ) ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[620]) ).
thf(647,plain,
! [SV30: $i,SV90: $i] :
( ( ( ! [SY484: $i] :
~ ~ ( ~ ( in @ SY484 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SY484 @ SV30 ) ) )
= $true )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(648,plain,
! [SV32: $i,SV92: $o,SV66: $i,SV81: $i] :
( ( ( in @ SV81 @ SV66 )
= $true )
| ( SV92 = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(649,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( in @ SV81 @ SV66 )
= $true )
| ( $true = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(650,plain,
! [SV32: $i,SV66: $i,SV81: $i] :
( ( ( in @ SV81 @ SV66 )
= $true )
| ( $false = $true )
| ( ( SV81 = SV32 )
= $true )
| ( ( in @ SV81 @ ( setadjoin @ SV32 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(651,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ! [SY388: $i] :
~ ( SV41 @ SY388 ) )
= $false )
| ( ( SV41 @ SV91 )
= $false )
| ( ( SV41 @ ( sK26_SY482 @ SV91 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(652,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ ( sK30_SY388 @ SV91 @ SV41 ) ) )
= $false )
| ( ( SV41 @ SV91 )
= $false )
| ( ( SV91
= ( sK26_SY482 @ SV91 @ SV41 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[632]) ).
thf(653,plain,
! [SV43: $i,SV103: $i] :
( ( ~ ( in @ SV103 @ ( sK3_SY390 @ SV43 ) )
| ! [SY504: $i] :
( ~ ( in @ SY504 @ SV103 )
| ( in @ SY504 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(654,plain,
! [SV43: $i,SV104: $i] :
( ( ! [SY505: $i] :
( ~ ~ ( ~ ( in @ SV104 @ SV43 )
| ~ ( in @ SY505 @ SV43 ) )
| ~ ! [SY506: $i] :
( ~ ( in @ SY506 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY506 )
| ( in @ SY505 @ SY506 ) )
| ~ ( ~ ( in @ SY505 @ SY506 )
| ( in @ SV104 @ SY506 ) ) ) )
| ( SV104 = SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(655,plain,
! [SV100: $i,SV43: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SV100 @ ( sK3_SY390 @ SV43 ) ) ) )
= $false )
| ( ( ! [SY500: $i] :
( ~ ( in @ SY500 @ SV99 )
| ( in @ SY500 @ SV100 ) )
| ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(656,plain,
! [SV95: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
| ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 ) )
= $false )
| ( ( ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[636]) ).
thf(657,plain,
! [SV10: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ omega ) )
= $true )
| ( ( in @ SV101 @ SV10 )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( in @ ( sK13_SY316 @ SV10 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(658,plain,
! [SV10: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ omega ) )
= $true )
| ( ( in @ SV102 @ SV10 )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( in @ ( sK13_SY316 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(659,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( ~ ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) ) )
= $true )
| ( ( ~ ! [SY495: $i] :
~ ~ ( ~ ( in @ SY495 @ SV54 )
| ~ ( SV16 @ SY495 @ SV98 ) ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(660,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( in @ SY496 @ SV54 )
| ~ ( SV16 @ SY496 @ SV98 ) ) )
= $true )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(661,plain,
! [SV93: $i,SV54: $i,SV16: $i > $i > $o] :
( ( ( ~ ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(662,plain,
! [SV16: $i > $i > $o,SV54: $i,SV93: $i] :
( ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(663,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ~ ( ~ ( SV22 @ ( sK32_SY347 @ SV87 @ SV22 ) )
| ~ ! [SY507: $i] :
( ~ ( SV22 @ SY507 )
| ( ( sK32_SY347 @ SV87 @ SV22 )
= SY507 ) ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[643]) ).
thf(664,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( ~ ( SV22 @ ( sK28_SY347 @ SV87 @ SV22 ) )
| ~ ! [SY502: $i] :
( ~ ( SV22 @ SY502 )
| ( ( sK28_SY347 @ SV87 @ SV22 )
= SY502 ) ) ) )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(665,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ~ ! [SY508: $i] :
~ ( ~ ( ~ ( SV23 @ SY508 )
| ( SY508
= ( sK33_SY351 @ SV88 @ SV23 ) ) )
| ~ ( ( SY508
!= ( sK33_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SY508 ) ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[645]) ).
thf(666,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ! [SY503: $i] :
~ ( ~ ( ~ ( SV23 @ SY503 )
| ( SY503
= ( sK29_SY351 @ SV88 @ SV23 ) ) )
| ~ ( ( SY503
!= ( sK29_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SY503 ) ) ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[646]) ).
thf(667,plain,
! [SV30: $i,SV90: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ( in @ SV105 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SV105 @ SV30 ) ) )
= $true )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(668,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ ( sK34_SY388 @ SV91 @ SV41 ) ) )
= $false )
| ( ( SV41 @ SV91 )
= $false )
| ( ( SV41 @ ( sK26_SY482 @ SV91 @ SV41 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[651]) ).
thf(669,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( SV41 @ ( sK30_SY388 @ SV91 @ SV41 ) )
= $true )
| ( ( SV41 @ SV91 )
= $false )
| ( ( SV91
= ( sK26_SY482 @ SV91 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(670,plain,
! [SV43: $i,SV103: $i] :
( ( ( ~ ( in @ SV103 @ ( sK3_SY390 @ SV43 ) ) )
= $true )
| ( ( ! [SY504: $i] :
( ~ ( in @ SY504 @ SV103 )
| ( in @ SY504 @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(671,plain,
! [SV106: $i,SV43: $i,SV104: $i] :
( ( ~ ~ ( ~ ( in @ SV104 @ SV43 )
| ~ ( in @ SV106 @ SV43 ) )
| ~ ! [SY509: $i] :
( ~ ( in @ SY509 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY509 )
| ( in @ SV106 @ SY509 ) )
| ~ ( ~ ( in @ SV106 @ SY509 )
| ( in @ SV104 @ SY509 ) ) ) )
| ( SV104 = SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(672,plain,
! [SV100: $i,SV43: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SV100 @ ( sK3_SY390 @ SV43 ) ) )
= $true )
| ( ( ! [SY500: $i] :
( ~ ( in @ SY500 @ SV99 )
| ( in @ SY500 @ SV100 ) )
| ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(673,plain,
! [SV95: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 ) )
= $false )
| ( ( ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(674,plain,
! [SV95: $i,SV43: $i] :
( ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(675,plain,
! [SV10: $i,SV101: $i] :
( ( ( in @ SV101 @ omega )
= $false )
| ( ( in @ SV101 @ SV10 )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( in @ ( sK13_SY316 @ SV10 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(676,plain,
! [SV10: $i,SV102: $i] :
( ( ( in @ SV102 @ omega )
= $false )
| ( ( in @ SV102 @ SV10 )
= $true )
| ( ( in @ emptyset @ SV10 )
= $false )
| ( ( in @ ( sK13_SY316 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(677,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $false )
| ( ( ~ ! [SY495: $i] :
~ ~ ( ~ ( in @ SY495 @ SV54 )
| ~ ( SV16 @ SY495 @ SV98 ) ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(678,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ! [SY496: $i] :
~ ~ ( ~ ( in @ SY496 @ SV54 )
| ~ ( SV16 @ SY496 @ SV98 ) ) )
= $false )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(679,plain,
! [SV93: $i,SV54: $i,SV16: $i > $i > $o] :
( ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( ~ ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(680,plain,
! [SV93: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(681,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( ~ ( SV22 @ ( sK32_SY347 @ SV87 @ SV22 ) )
| ~ ! [SY507: $i] :
( ~ ( SV22 @ SY507 )
| ( ( sK32_SY347 @ SV87 @ SV22 )
= SY507 ) ) ) )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(682,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ ( sK28_SY347 @ SV87 @ SV22 ) )
| ~ ! [SY502: $i] :
( ~ ( SV22 @ SY502 )
| ( ( sK28_SY347 @ SV87 @ SV22 )
= SY502 ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(683,plain,
! [SV88: $i,SV23: $i > $o] :
( ( ( ! [SY508: $i] :
~ ( ~ ( ~ ( SV23 @ SY508 )
| ( SY508
= ( sK33_SY351 @ SV88 @ SV23 ) ) )
| ~ ( ( SY508
!= ( sK33_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SY508 ) ) ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[665]) ).
thf(684,plain,
! [SV88: $i,SV107: $i,SV23: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV23 @ SV107 )
| ( SV107
= ( sK29_SY351 @ SV88 @ SV23 ) ) )
| ~ ( ( SV107
!= ( sK29_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SV107 ) ) ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(685,plain,
! [SV30: $i,SV90: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ SV105 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SV105 @ SV30 ) ) )
= $false )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(686,plain,
! [SV91: $i,SV41: $i > $o] :
( ( ( SV41 @ ( sK34_SY388 @ SV91 @ SV41 ) )
= $true )
| ( ( SV41 @ SV91 )
= $false )
| ( ( SV41 @ ( sK26_SY482 @ SV91 @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(687,plain,
! [SV43: $i,SV103: $i] :
( ( ( in @ SV103 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( ! [SY504: $i] :
( ~ ( in @ SY504 @ SV103 )
| ( in @ SY504 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(688,plain,
! [SV106: $i,SV43: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( in @ SV104 @ SV43 )
| ~ ( in @ SV106 @ SV43 ) ) )
= $true )
| ( ( ~ ! [SY509: $i] :
( ~ ( in @ SY509 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY509 )
| ( in @ SV106 @ SY509 ) )
| ~ ( ~ ( in @ SV106 @ SY509 )
| ( in @ SV104 @ SY509 ) ) ) )
| ( SV104 = SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(689,plain,
! [SV100: $i,SV43: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ ( sK3_SY390 @ SV43 ) ) )
= $true )
| ( ( ~ ( in @ SV100 @ ( sK3_SY390 @ SV43 ) ) )
= $true )
| ( ( ! [SY500: $i] :
( ~ ( in @ SY500 @ SV99 )
| ( in @ SY500 @ SV100 ) )
| ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(690,plain,
! [SV95: $i,SV43: $i] :
( ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( ~ ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[673]) ).
thf(691,plain,
! [SV43: $i,SV95: $i] :
( ( ( ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(692,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY495: $i] :
~ ~ ( ~ ( in @ SY495 @ SV54 )
| ~ ( SV16 @ SY495 @ SV98 ) ) )
= $false )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(693,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY496: $i] :
~ ~ ( ~ ( in @ SY496 @ SV54 )
| ~ ( SV16 @ SY496 @ SV98 ) ) )
= $true )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(694,plain,
! [SV93: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY423: $i] :
~ ! [SY424: $i] :
~ ( ~ ( ~ ( in @ SY424 @ SY423 )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY424 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY424 ) )
| ( in @ SY424 @ SY423 ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(695,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i] :
( ( ( ~ ! [SY510: $i] :
~ ( ~ ( ~ ( in @ SY510 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY510 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY510 ) )
| ( in @ SY510 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[680]) ).
thf(696,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ ( sK32_SY347 @ SV87 @ SV22 ) )
| ~ ! [SY507: $i] :
( ~ ( SV22 @ SY507 )
| ( ( sK32_SY347 @ SV87 @ SV22 )
= SY507 ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(697,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ ( sK28_SY347 @ SV87 @ SV22 ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(698,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ! [SY502: $i] :
( ~ ( SV22 @ SY502 )
| ( ( sK28_SY347 @ SV87 @ SV22 )
= SY502 ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(699,plain,
! [SV88: $i,SV108: $i,SV23: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV23 @ SV108 )
| ( SV108
= ( sK33_SY351 @ SV88 @ SV23 ) ) )
| ~ ( ( SV108
!= ( sK33_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SV108 ) ) ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(700,plain,
! [SV88: $i,SV107: $i,SV23: $i > $o] :
( ( ( ~ ( ~ ( SV23 @ SV107 )
| ( SV107
= ( sK29_SY351 @ SV88 @ SV23 ) ) )
| ~ ( ( SV107
!= ( sK29_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SV107 ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(701,plain,
! [SV30: $i,SV90: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ ( sK17_SY366 @ SV90 @ SV30 ) )
| ~ ( in @ SV105 @ SV30 ) )
= $true )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(702,plain,
! [SV43: $i,SV103: $i,SV109: $i] :
( ( ( ~ ( in @ SV109 @ SV103 )
| ( in @ SV109 @ SV43 ) )
= $true )
| ( ( in @ SV103 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(703,plain,
! [SV106: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ SV104 @ SV43 )
| ~ ( in @ SV106 @ SV43 ) ) )
= $false )
| ( ( ~ ! [SY509: $i] :
( ~ ( in @ SY509 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY509 )
| ( in @ SV106 @ SY509 ) )
| ~ ( ~ ( in @ SV106 @ SY509 )
| ( in @ SV104 @ SY509 ) ) ) )
| ( SV104 = SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(704,plain,
! [SV100: $i,SV43: $i,SV99: $i] :
( ( ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( ~ ( in @ SV100 @ ( sK3_SY390 @ SV43 ) ) )
= $true )
| ( ( ! [SY500: $i] :
( ~ ( in @ SY500 @ SV99 )
| ( in @ SY500 @ SV100 ) )
| ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(705,plain,
! [SV43: $i,SV95: $i] :
( ( ( ~ ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(706,plain,
! [SV43: $i,SV95: $i] :
( ( ( ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(707,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV54 )
| ~ ( SV16 @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV98 ) ) )
= $false )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[692]) ).
thf(708,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i,SV110: $i] :
( ( ( ~ ~ ( ~ ( in @ SV110 @ SV54 )
| ~ ( SV16 @ SV110 @ SV98 ) ) )
= $true )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(709,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i] :
( ( ( ~ ! [SY513: $i] :
~ ( ~ ( ~ ( in @ SY513 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY513 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY513 ) )
| ( in @ SY513 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[694]) ).
thf(710,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i] :
( ( ( ! [SY510: $i] :
~ ( ~ ( ~ ( in @ SY510 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY510 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY510 ) )
| ( in @ SY510 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) ) ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(711,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ ( sK32_SY347 @ SV87 @ SV22 ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(712,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ~ ! [SY507: $i] :
( ~ ( SV22 @ SY507 )
| ( ( sK32_SY347 @ SV87 @ SV22 )
= SY507 ) ) )
= $false )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(713,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( SV22 @ ( sK28_SY347 @ SV87 @ SV22 ) )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(714,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ! [SY502: $i] :
( ~ ( SV22 @ SY502 )
| ( ( sK28_SY347 @ SV87 @ SV22 )
= SY502 ) ) )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(715,plain,
! [SV88: $i,SV108: $i,SV23: $i > $o] :
( ( ( ~ ( ~ ( SV23 @ SV108 )
| ( SV108
= ( sK33_SY351 @ SV88 @ SV23 ) ) )
| ~ ( ( SV108
!= ( sK33_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SV108 ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(716,plain,
! [SV88: $i,SV107: $i,SV23: $i > $o] :
( ( ( ~ ( ~ ( SV23 @ SV107 )
| ( SV107
= ( sK29_SY351 @ SV88 @ SV23 ) ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(717,plain,
! [SV23: $i > $o,SV88: $i,SV107: $i] :
( ( ( ~ ( ( SV107
!= ( sK29_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SV107 ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(718,plain,
! [SV30: $i,SV90: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ ( sK17_SY366 @ SV90 @ SV30 ) ) )
= $true )
| ( ( ~ ( in @ SV105 @ SV30 ) )
= $true )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(719,plain,
! [SV43: $i,SV103: $i,SV109: $i] :
( ( ( ~ ( in @ SV109 @ SV103 ) )
= $true )
| ( ( in @ SV109 @ SV43 )
= $true )
| ( ( in @ SV103 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(720,plain,
! [SV106: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV43 )
| ~ ( in @ SV106 @ SV43 ) )
= $true )
| ( ( ~ ! [SY509: $i] :
( ~ ( in @ SY509 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY509 )
| ( in @ SV106 @ SY509 ) )
| ~ ( ~ ( in @ SV106 @ SY509 )
| ( in @ SV104 @ SY509 ) ) ) )
| ( SV104 = SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[703]) ).
thf(721,plain,
! [SV99: $i,SV43: $i,SV100: $i] :
( ( ( in @ SV100 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( ! [SY500: $i] :
( ~ ( in @ SY500 @ SV99 )
| ( in @ SY500 @ SV100 ) )
| ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(722,plain,
! [SV43: $i,SV95: $i] :
( ( ( ! [SY486: $i] :
~ ( in @ SY486 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(723,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ( in @ SV111 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(724,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV54 )
| ~ ( SV16 @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV98 ) ) )
= $true )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(725,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i,SV110: $i] :
( ( ( ~ ( ~ ( in @ SV110 @ SV54 )
| ~ ( SV16 @ SV110 @ SV98 ) ) )
= $false )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(726,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i] :
( ( ( ! [SY513: $i] :
~ ( ~ ( ~ ( in @ SY513 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY425: $i] :
~ ~ ( ~ ( in @ SY425 @ SV54 )
| ~ ( SV16 @ SY425 @ SY513 ) ) )
| ~ ( ~ ~ ! [SY426: $i] :
~ ~ ( ~ ( in @ SY426 @ SV54 )
| ~ ( SV16 @ SY426 @ SY513 ) )
| ( in @ SY513 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) ) ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(727,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV112: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ SY516 @ SV54 )
| ~ ( SV16 @ SY516 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY517: $i] :
~ ~ ( ~ ( in @ SY517 @ SV54 )
| ~ ( SV16 @ SY517 @ SV112 ) )
| ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) ) ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(728,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( SV22 @ ( sK32_SY347 @ SV87 @ SV22 ) )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(729,plain,
! [SV87: $i,SV22: $i > $o] :
( ( ( ! [SY507: $i] :
( ~ ( SV22 @ SY507 )
| ( ( sK32_SY347 @ SV87 @ SV22 )
= SY507 ) ) )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(730,plain,
! [SV87: $i,SV113: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ SV113 )
| ( ( sK28_SY347 @ SV87 @ SV22 )
= SV113 ) )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(731,plain,
! [SV88: $i,SV108: $i,SV23: $i > $o] :
( ( ( ~ ( ~ ( SV23 @ SV108 )
| ( SV108
= ( sK33_SY351 @ SV88 @ SV23 ) ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(732,plain,
! [SV23: $i > $o,SV88: $i,SV108: $i] :
( ( ( ~ ( ( SV108
!= ( sK33_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SV108 ) ) )
= $false )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(733,plain,
! [SV88: $i,SV107: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ SV107 )
| ( SV107
= ( sK29_SY351 @ SV88 @ SV23 ) ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(734,plain,
! [SV23: $i > $o,SV88: $i,SV107: $i] :
( ( ( ( SV107
!= ( sK29_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SV107 ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(735,plain,
! [SV30: $i,SV90: $i,SV105: $i] :
( ( ( in @ SV105 @ ( sK17_SY366 @ SV90 @ SV30 ) )
= $false )
| ( ( ~ ( in @ SV105 @ SV30 ) )
= $true )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(736,plain,
! [SV43: $i,SV103: $i,SV109: $i] :
( ( ( in @ SV109 @ SV103 )
= $false )
| ( ( in @ SV109 @ SV43 )
= $true )
| ( ( in @ SV103 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(737,plain,
! [SV106: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV43 ) )
= $true )
| ( ( ~ ( in @ SV106 @ SV43 ) )
= $true )
| ( ( ~ ! [SY509: $i] :
( ~ ( in @ SY509 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY509 )
| ( in @ SV106 @ SY509 ) )
| ~ ( ~ ( in @ SV106 @ SY509 )
| ( in @ SV104 @ SY509 ) ) ) )
| ( SV104 = SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(738,plain,
! [SV43: $i,SV100: $i,SV99: $i] :
( ( ( ! [SY500: $i] :
( ~ ( in @ SY500 @ SV99 )
| ( in @ SY500 @ SV100 ) ) )
= $true )
| ( ( ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true )
| ( ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ SV100 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(739,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(740,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( in @ SV111 @ SV95 )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(741,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( ~ ( in @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV54 )
| ~ ( SV16 @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV98 ) )
= $false )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(742,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ SV54 )
| ~ ( SV16 @ SV110 @ SV98 ) )
= $true )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(743,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV115: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY518: $i] :
~ ~ ( ~ ( in @ SY518 @ SV54 )
| ~ ( SV16 @ SY518 @ SV115 ) ) )
| ~ ( ~ ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ SY519 @ SV54 )
| ~ ( SV16 @ SY519 @ SV115 ) )
| ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) ) ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(744,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV112: $i] :
( ( ( ~ ( ~ ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ SY516 @ SV54 )
| ~ ( SV16 @ SY516 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY517: $i] :
~ ~ ( ~ ( in @ SY517 @ SV54 )
| ~ ( SV16 @ SY517 @ SV112 ) )
| ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(745,plain,
! [SV87: $i,SV116: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ SV116 )
| ( ( sK32_SY347 @ SV87 @ SV22 )
= SV116 ) )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(746,plain,
! [SV87: $i,SV113: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ SV113 ) )
= $true )
| ( ( ( sK28_SY347 @ SV87 @ SV22 )
= SV113 )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(747,plain,
! [SV88: $i,SV108: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ SV108 )
| ( SV108
= ( sK33_SY351 @ SV88 @ SV23 ) ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(748,plain,
! [SV23: $i > $o,SV88: $i,SV108: $i] :
( ( ( ( SV108
!= ( sK33_SY351 @ SV88 @ SV23 ) )
| ( SV23 @ SV108 ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(749,plain,
! [SV88: $i,SV107: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ SV107 ) )
= $true )
| ( ( SV107
= ( sK29_SY351 @ SV88 @ SV23 ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(750,plain,
! [SV23: $i > $o,SV88: $i,SV107: $i] :
( ( ( SV107
!= ( sK29_SY351 @ SV88 @ SV23 ) )
= $true )
| ( ( SV23 @ SV107 )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(751,plain,
! [SV90: $i,SV30: $i,SV105: $i] :
( ( ( in @ SV105 @ SV30 )
= $false )
| ( ( in @ SV105 @ ( sK17_SY366 @ SV90 @ SV30 ) )
= $false )
| ( ( in @ SV90 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(752,plain,
! [SV106: $i,SV43: $i,SV104: $i] :
( ( ( in @ SV104 @ SV43 )
= $false )
| ( ( ~ ( in @ SV106 @ SV43 ) )
= $true )
| ( ( ~ ! [SY509: $i] :
( ~ ( in @ SY509 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY509 )
| ( in @ SV106 @ SY509 ) )
| ~ ( ~ ( in @ SV106 @ SY509 )
| ( in @ SV104 @ SY509 ) ) ) )
| ( SV104 = SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(753,plain,
! [SV43: $i,SV100: $i,SV99: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV99 )
| ( in @ SV117 @ SV100 ) )
= $true )
| ( ( ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true )
| ( ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ SV100 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(754,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( in @ SV114 @ SV95 )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( ~ ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(755,plain,
! [SV111: $i,SV95: $i,SV43: $i] :
( ( ( ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(756,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( ~ ( in @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV54 ) )
= $false )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(757,plain,
! [SV54: $i,SV98: $i,SV16: $i > $i > $o] :
( ( ( ~ ( SV16 @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV98 ) )
= $false )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(758,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ SV54 ) )
= $true )
| ( ( ~ ( SV16 @ SV110 @ SV98 ) )
= $true )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(759,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY518: $i] :
~ ~ ( ~ ( in @ SY518 @ SV54 )
| ~ ( SV16 @ SY518 @ SV115 ) ) )
| ~ ( ~ ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ SY519 @ SV54 )
| ~ ( SV16 @ SY519 @ SV115 ) )
| ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(760,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV112: $i] :
( ( ( ~ ( ~ ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ SY516 @ SV54 )
| ~ ( SV16 @ SY516 @ SV112 ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(761,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ( ~ ~ ! [SY517: $i] :
~ ~ ( ~ ( in @ SY517 @ SV54 )
| ~ ( SV16 @ SY517 @ SV112 ) )
| ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(762,plain,
! [SV87: $i,SV116: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ SV116 ) )
= $true )
| ( ( ( sK32_SY347 @ SV87 @ SV22 )
= SV116 )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(763,plain,
! [SV87: $i,SV113: $i,SV22: $i > $o] :
( ( ( SV22 @ SV113 )
= $false )
| ( ( ( sK28_SY347 @ SV87 @ SV22 )
= SV113 )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV87
= ( sK24_SY479 @ SV87 @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(764,plain,
! [SV88: $i,SV108: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ SV108 ) )
= $true )
| ( ( SV108
= ( sK33_SY351 @ SV88 @ SV23 ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(765,plain,
! [SV23: $i > $o,SV88: $i,SV108: $i] :
( ( ( SV108
!= ( sK33_SY351 @ SV88 @ SV23 ) )
= $true )
| ( ( SV23 @ SV108 )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(766,plain,
! [SV88: $i,SV107: $i,SV23: $i > $o] :
( ( ( SV23 @ SV107 )
= $false )
| ( ( SV107
= ( sK29_SY351 @ SV88 @ SV23 ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(767,plain,
! [SV23: $i > $o,SV88: $i,SV107: $i] :
( ( ( SV107
= ( sK29_SY351 @ SV88 @ SV23 ) )
= $false )
| ( ( SV23 @ SV107 )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV88
= ( sK25_SY480 @ SV88 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(768,plain,
! [SV104: $i,SV43: $i,SV106: $i] :
( ( ( in @ SV106 @ SV43 )
= $false )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( ~ ! [SY509: $i] :
( ~ ( in @ SY509 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY509 )
| ( in @ SV106 @ SY509 ) )
| ~ ( ~ ( in @ SV106 @ SY509 )
| ( in @ SV104 @ SY509 ) ) ) )
| ( SV104 = SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(769,plain,
! [SV43: $i,SV100: $i,SV99: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV99 ) )
= $true )
| ( ( in @ SV117 @ SV100 )
= $true )
| ( ( ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true )
| ( ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ SV100 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(770,plain,
! [SV114: $i,SV95: $i,SV43: $i] :
( ( ( ! [SY487: $i] :
~ ~ ! [SY488: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY487 @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY488 @ SV95 ) )
| ~ ~ ~ ! [SY489: $i] :
~ ~ ( ~ ( in @ SY489 @ SY487 )
| ~ ( in @ SY489 @ SV95 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK3_SY390 @ SV43 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY474 )
| ( in @ SX6 @ SY487 ) )
| ( in @ SY488 @ SY474 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(771,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY520 @ SV95 ) )
| ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
| ~ ! [SY522: $i] :
( ~ ( in @ SY522 @ ( sK3_SY390 @ SV43 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY522 )
| ( in @ SY523 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ SY520 @ SY522 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[755]) ).
thf(772,plain,
! [SV54: $i,SV16: $i > $i > $o,SV98: $i] :
( ( ( in @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV54 )
= $true )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(773,plain,
! [SV54: $i,SV98: $i,SV16: $i > $i > $o] :
( ( ( SV16 @ ( sK36_SY495 @ SV98 @ SV16 @ SV54 ) @ SV98 )
= $true )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $false )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(774,plain,
! [SV98: $i,SV16: $i > $i > $o,SV54: $i,SV110: $i] :
( ( ( in @ SV110 @ SV54 )
= $false )
| ( ( ~ ( SV16 @ SV110 @ SV98 ) )
= $true )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(775,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY518: $i] :
~ ~ ( ~ ( in @ SY518 @ SV54 )
| ~ ( SV16 @ SY518 @ SV115 ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(776,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ( ~ ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ SY519 @ SV54 )
| ~ ( SV16 @ SY519 @ SV115 ) )
| ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) ) ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(777,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV112: $i] :
( ( ( ~ ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ SY516 @ SV54 )
| ~ ( SV16 @ SY516 @ SV112 ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(778,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ~ ! [SY517: $i] :
~ ~ ( ~ ( in @ SY517 @ SV54 )
| ~ ( SV16 @ SY517 @ SV112 ) )
| ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(779,plain,
! [SV87: $i,SV116: $i,SV22: $i > $o] :
( ( ( SV22 @ SV116 )
= $false )
| ( ( ( sK32_SY347 @ SV87 @ SV22 )
= SV116 )
= $true )
| ( ( SV22 @ SV87 )
= $false )
| ( ( SV22 @ ( sK24_SY479 @ SV87 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(780,plain,
! [SV88: $i,SV108: $i,SV23: $i > $o] :
( ( ( SV23 @ SV108 )
= $false )
| ( ( SV108
= ( sK33_SY351 @ SV88 @ SV23 ) )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(781,plain,
! [SV23: $i > $o,SV88: $i,SV108: $i] :
( ( ( SV108
= ( sK33_SY351 @ SV88 @ SV23 ) )
= $false )
| ( ( SV23 @ SV108 )
= $true )
| ( ( SV23 @ SV88 )
= $false )
| ( ( SV23 @ ( sK25_SY480 @ SV88 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(782,plain,
! [SV106: $i,SV104: $i,SV43: $i] :
( ( ( ~ ! [SY509: $i] :
( ~ ( in @ SY509 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY509 )
| ( in @ SV106 @ SY509 ) )
| ~ ( ~ ( in @ SV106 @ SY509 )
| ( in @ SV104 @ SY509 ) ) ) ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(783,plain,
! [SV43: $i,SV100: $i,SV99: $i,SV117: $i] :
( ( ( in @ SV117 @ SV99 )
= $false )
| ( ( in @ SV117 @ SV100 )
= $true )
| ( ( ! [SY501: $i] :
( ~ ( in @ SY501 @ SV100 )
| ( in @ SY501 @ SV99 ) ) )
= $true )
| ( ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ SV100 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(784,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ~ ! [SY524: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY524 @ SV95 ) )
| ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
| ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ ( sK3_SY390 @ SV43 ) )
| ! [SY527: $i] :
( ~ ( in @ SY527 @ SY526 )
| ( in @ SY527 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ SY524 @ SY526 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[770]) ).
thf(785,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ! [SY520: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY520 @ SV95 ) )
| ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
| ~ ! [SY522: $i] :
( ~ ( in @ SY522 @ ( sK3_SY390 @ SV43 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY522 )
| ( in @ SY523 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ SY520 @ SY522 ) ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(786,plain,
! [SV54: $i,SV98: $i,SV110: $i,SV16: $i > $i > $o] :
( ( ( SV16 @ SV110 @ SV98 )
= $false )
| ( ( in @ SV110 @ SV54 )
= $false )
| ( ( in @ SV98 @ ( sK20_SY423 @ SV16 @ SV54 ) )
= $true )
| ( ( in @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(787,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
| ~ ! [SY518: $i] :
~ ~ ( ~ ( in @ SY518 @ SV54 )
| ~ ( SV16 @ SY518 @ SV115 ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(788,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ SY519 @ SV54 )
| ~ ( SV16 @ SY519 @ SV115 ) )
| ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(789,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV112: $i] :
( ( ( ~ ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) ) )
= $true )
| ( ( ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ SY516 @ SV54 )
| ~ ( SV16 @ SY516 @ SV112 ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(790,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ~ ! [SY517: $i] :
~ ~ ( ~ ( in @ SY517 @ SV54 )
| ~ ( SV16 @ SY517 @ SV112 ) ) )
= $true )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(791,plain,
! [SV106: $i,SV104: $i,SV43: $i] :
( ( ( ! [SY509: $i] :
( ~ ( in @ SY509 @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ SY509 )
| ( in @ SV106 @ SY509 ) )
| ~ ( ~ ( in @ SV106 @ SY509 )
| ( in @ SV104 @ SY509 ) ) ) ) )
= $false )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(792,plain,
! [SV43: $i,SV117: $i,SV99: $i,SV100: $i,SV118: $i] :
( ( ( ~ ( in @ SV118 @ SV100 )
| ( in @ SV118 @ SV99 ) )
= $true )
| ( ( in @ SV117 @ SV100 )
= $true )
| ( ( in @ SV117 @ SV99 )
= $false )
| ( ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ SV100 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(793,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ! [SY524: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY524 @ SV95 ) )
| ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
| ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ ( sK3_SY390 @ SV43 ) )
| ! [SY527: $i] :
( ~ ( in @ SY527 @ SY526 )
| ( in @ SY527 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ SY524 @ SY526 ) ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(794,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ! [SY520: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY520 @ SV95 ) )
| ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
| ~ ! [SY522: $i] :
( ~ ( in @ SY522 @ ( sK3_SY390 @ SV43 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY522 )
| ( in @ SY523 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ SY520 @ SY522 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(795,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) ) )
= $true )
| ( ( ~ ! [SY518: $i] :
~ ~ ( ~ ( in @ SY518 @ SV54 )
| ~ ( SV16 @ SY518 @ SV115 ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(796,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ SY519 @ SV54 )
| ~ ( SV16 @ SY519 @ SV115 ) ) )
= $true )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(797,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV112: $i] :
( ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ SY516 @ SV54 )
| ~ ( SV16 @ SY516 @ SV112 ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(798,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ! [SY517: $i] :
~ ~ ( ~ ( in @ SY517 @ SV54 )
| ~ ( SV16 @ SY517 @ SV112 ) ) )
= $false )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(799,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( ~ ( in @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( ~ ( ~ ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) )
| ~ ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) ) ) )
= $false )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[791]) ).
thf(800,plain,
! [SV43: $i,SV117: $i,SV99: $i,SV100: $i,SV118: $i] :
( ( ( ~ ( in @ SV118 @ SV100 ) )
= $true )
| ( ( in @ SV118 @ SV99 )
= $true )
| ( ( in @ SV117 @ SV100 )
= $true )
| ( ( in @ SV117 @ SV99 )
= $false )
| ( ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ SV100 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(801,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ! [SY524: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ SY524 @ SV95 ) )
| ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
| ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ ( sK3_SY390 @ SV43 ) )
| ! [SY527: $i] :
( ~ ( in @ SY527 @ SY526 )
| ( in @ SY527 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ SY524 @ SY526 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(802,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) )
| ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
| ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ ( sK3_SY390 @ SV43 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY529 )
| ( in @ SY523 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SY529 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[794]) ).
thf(803,plain,
! [SV54: $i,SV16: $i > $i > $o,SV93: $i,SV115: $i] :
( ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( ~ ! [SY518: $i] :
~ ~ ( ~ ( in @ SY518 @ SV54 )
| ~ ( SV16 @ SY518 @ SV115 ) ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(804,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ SY519 @ SV54 )
| ~ ( SV16 @ SY519 @ SV115 ) ) )
= $false )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(805,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY516: $i] :
~ ~ ( ~ ( in @ SY516 @ SV54 )
| ~ ( SV16 @ SY516 @ SV112 ) ) )
= $false )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(806,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY517: $i] :
~ ~ ( ~ ( in @ SY517 @ SV54 )
| ~ ( SV16 @ SY517 @ SV112 ) ) )
= $true )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(807,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( ~ ( in @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) @ ( sK3_SY390 @ SV43 ) ) )
= $false )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(808,plain,
! [SV43: $i,SV106: $i,SV104: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) )
| ~ ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) ) ) )
= $false )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(809,plain,
! [SV43: $i,SV117: $i,SV99: $i,SV100: $i,SV118: $i] :
( ( ( in @ SV118 @ SV100 )
= $false )
| ( ( in @ SV118 @ SV99 )
= $true )
| ( ( in @ SV117 @ SV100 )
= $true )
| ( ( in @ SV117 @ SV99 )
= $false )
| ( ( in @ SV99 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ SV100 @ ( sK3_SY390 @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(810,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) )
| ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
| ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ ( sK3_SY390 @ SV43 ) )
| ! [SY527: $i] :
( ~ ( in @ SY527 @ SY532 )
| ( in @ SY527 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SY532 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[801]) ).
thf(811,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) )
| ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
| ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ ( sK3_SY390 @ SV43 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY529 )
| ( in @ SY523 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SY529 ) ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(812,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY518: $i] :
~ ~ ( ~ ( in @ SY518 @ SV54 )
| ~ ( SV16 @ SY518 @ SV115 ) ) )
= $false )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(813,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i] :
( ( ( ! [SY519: $i] :
~ ~ ( ~ ( in @ SY519 @ SV54 )
| ~ ( SV16 @ SY519 @ SV115 ) ) )
= $true )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(814,plain,
! [SV54: $i,SV16: $i > $i > $o,SV112: $i,SV93: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV54 )
| ~ ( SV16 @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV112 ) ) )
= $false )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[805]) ).
thf(815,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i,SV119: $i] :
( ( ( ~ ~ ( ~ ( in @ SV119 @ SV54 )
| ~ ( SV16 @ SV119 @ SV112 ) ) )
= $true )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(816,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( in @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(817,plain,
! [SV43: $i,SV106: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) )
| ~ ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(818,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) )
| ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
| ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ ( sK3_SY390 @ SV43 ) )
| ! [SY527: $i] :
( ~ ( in @ SY527 @ SY532 )
| ( in @ SY527 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SY532 ) ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(819,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) )
| ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
| ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ ( sK3_SY390 @ SV43 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY529 )
| ( in @ SY523 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SY529 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(820,plain,
! [SV54: $i,SV16: $i > $i > $o,SV115: $i,SV93: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV54 )
| ~ ( SV16 @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV115 ) ) )
= $false )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[812]) ).
thf(821,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ( in @ SV120 @ SV54 )
| ~ ( SV16 @ SV120 @ SV115 ) ) )
= $true )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(822,plain,
! [SV54: $i,SV16: $i > $i > $o,SV112: $i,SV93: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV54 )
| ~ ( SV16 @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV112 ) ) )
= $true )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(823,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i,SV119: $i] :
( ( ( ~ ( ~ ( in @ SV119 @ SV54 )
| ~ ( SV16 @ SV119 @ SV112 ) ) )
= $false )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(824,plain,
! [SV43: $i,SV106: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(825,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) )
| ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
| ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ ( sK3_SY390 @ SV43 ) )
| ! [SY527: $i] :
( ~ ( in @ SY527 @ SY532 )
| ( in @ SY527 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SY532 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(826,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) )
| ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(827,plain,
! [SV95: $i,SV111: $i,SV43: $i] :
( ( ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ ( sK3_SY390 @ SV43 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY529 )
| ( in @ SY523 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SY529 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(828,plain,
! [SV54: $i,SV16: $i > $i > $o,SV115: $i,SV93: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV54 )
| ~ ( SV16 @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV115 ) ) )
= $true )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(829,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i,SV120: $i] :
( ( ( ~ ( ~ ( in @ SV120 @ SV54 )
| ~ ( SV16 @ SV120 @ SV115 ) ) )
= $false )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(830,plain,
! [SV54: $i,SV16: $i > $i > $o,SV112: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV54 )
| ~ ( SV16 @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV112 ) )
= $false )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(831,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV54 )
| ~ ( SV16 @ SV119 @ SV112 ) )
= $true )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(832,plain,
! [SV43: $i,SV106: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(833,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) )
| ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(834,plain,
! [SV95: $i,SV114: $i,SV43: $i] :
( ( ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ ( sK3_SY390 @ SV43 ) )
| ! [SY527: $i] :
( ~ ( in @ SY527 @ SY532 )
| ( in @ SY527 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SY532 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(835,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) )
| ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(836,plain,
! [SV95: $i,SV111: $i,SV43: $i] :
( ( ( ! [SY529: $i] :
( ~ ( in @ SY529 @ ( sK3_SY390 @ SV43 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY529 )
| ( in @ SY523 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SY529 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(837,plain,
! [SV54: $i,SV16: $i > $i > $o,SV115: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV54 )
| ~ ( SV16 @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV115 ) )
= $false )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(838,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV54 )
| ~ ( SV16 @ SV120 @ SV115 ) )
= $true )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(839,plain,
! [SV54: $i,SV16: $i > $i > $o,SV112: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV54 ) )
= $false )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(840,plain,
! [SV54: $i,SV112: $i,SV93: $i,SV16: $i > $i > $o] :
( ( ( ~ ( SV16 @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV112 ) )
= $false )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(841,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV54 ) )
= $true )
| ( ( ~ ( SV16 @ SV119 @ SV112 ) )
= $true )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(842,plain,
! [SV43: $i,SV106: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(843,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(844,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) )
| ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(845,plain,
! [SV95: $i,SV114: $i,SV43: $i] :
( ( ( ! [SY532: $i] :
( ~ ( in @ SY532 @ ( sK3_SY390 @ SV43 ) )
| ! [SY527: $i] :
( ~ ( in @ SY527 @ SY532 )
| ( in @ SY527 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SY532 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[834]) ).
thf(846,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) )
| ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(847,plain,
! [SV95: $i,SV111: $i,SV43: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ ( sK3_SY390 @ SV43 ) )
| ! [SY534: $i] :
( ~ ( in @ SY534 @ SV121 )
| ( in @ SY534 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV121 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(848,plain,
! [SV54: $i,SV16: $i > $i > $o,SV115: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV54 ) )
= $false )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[837]) ).
thf(849,plain,
! [SV54: $i,SV115: $i,SV93: $i,SV16: $i > $i > $o] :
( ( ( ~ ( SV16 @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV115 ) )
= $false )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[837]) ).
thf(850,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV54 ) )
= $true )
| ( ( ~ ( SV16 @ SV120 @ SV115 ) )
= $true )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(851,plain,
! [SV54: $i,SV16: $i > $i > $o,SV112: $i,SV93: $i] :
( ( ( in @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV54 )
= $true )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(852,plain,
! [SV54: $i,SV112: $i,SV93: $i,SV16: $i > $i > $o] :
( ( ( SV16 @ ( sK43_SY516 @ SV93 @ SV112 @ SV16 @ SV54 ) @ SV112 )
= $true )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(853,plain,
! [SV93: $i,SV112: $i,SV16: $i > $i > $o,SV54: $i,SV119: $i] :
( ( ( in @ SV119 @ SV54 )
= $false )
| ( ( ~ ( SV16 @ SV119 @ SV112 ) )
= $true )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(854,plain,
! [SV43: $i,SV106: $i,SV104: $i] :
( ( ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(855,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) )
= $false )
| ( ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $false )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(856,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) )
| ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(857,plain,
! [SV95: $i,SV114: $i,SV43: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ ( sK3_SY390 @ SV43 ) )
| ! [SY535: $i] :
( ~ ( in @ SY535 @ SV122 )
| ( in @ SY535 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV122 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(858,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(859,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(860,plain,
! [SV95: $i,SV111: $i,SV43: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ ( sK3_SY390 @ SV43 ) ) )
= $true )
| ( ( ! [SY534: $i] :
( ~ ( in @ SY534 @ SV121 )
| ( in @ SY534 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV121 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(861,plain,
! [SV54: $i,SV16: $i > $i > $o,SV115: $i,SV93: $i] :
( ( ( in @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV54 )
= $true )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(862,plain,
! [SV54: $i,SV115: $i,SV93: $i,SV16: $i > $i > $o] :
( ( ( SV16 @ ( sK44_SY518 @ SV93 @ SV115 @ SV16 @ SV54 ) @ SV115 )
= $true )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(863,plain,
! [SV93: $i,SV115: $i,SV16: $i > $i > $o,SV54: $i,SV120: $i] :
( ( ( in @ SV120 @ SV54 )
= $false )
| ( ( ~ ( SV16 @ SV120 @ SV115 ) )
= $true )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(864,plain,
! [SV93: $i,SV54: $i,SV112: $i,SV119: $i,SV16: $i > $i > $o] :
( ( ( SV16 @ SV119 @ SV112 )
= $false )
| ( ( in @ SV119 @ SV54 )
= $false )
| ( ( in @ SV112 @ ( sK35_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV93
= ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(865,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
| ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) )
= $false )
| ( ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(866,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) )
= $false )
| ( ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $false )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(867,plain,
! [SV43: $i,SV106: $i,SV104: $i] :
( ( ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $false )
| ( ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $false )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(868,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(869,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(870,plain,
! [SV95: $i,SV114: $i,SV43: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ ( sK3_SY390 @ SV43 ) ) )
= $true )
| ( ( ! [SY535: $i] :
( ~ ( in @ SY535 @ SV122 )
| ( in @ SY535 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV122 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(871,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(872,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(873,plain,
! [SV95: $i,SV111: $i,SV43: $i,SV121: $i] :
( ( ( in @ SV121 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( ! [SY534: $i] :
( ~ ( in @ SY534 @ SV121 )
| ( in @ SY534 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
| ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV121 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(874,plain,
! [SV93: $i,SV54: $i,SV115: $i,SV120: $i,SV16: $i > $i > $o] :
( ( ( SV16 @ SV120 @ SV115 )
= $false )
| ( ( in @ SV120 @ SV54 )
= $false )
| ( ( in @ SV115 @ ( sK37_SY423 @ SV93 @ SV16 @ SV54 ) )
= $true )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ SV93 )
= $false )
| ( ( SV16 @ ( sK8_SY420 @ SV16 @ SV54 ) @ ( sK27_SY483 @ SV93 @ SV54 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(875,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) ) )
= $false )
| ( ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(876,plain,
! [SV43: $i,SV106: $i,SV104: $i] :
( ( ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $false )
| ( ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(877,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $true )
| ( ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $false )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(878,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(879,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(880,plain,
! [SV95: $i,SV114: $i,SV43: $i,SV122: $i] :
( ( ( in @ SV122 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( ! [SY535: $i] :
( ~ ( in @ SY535 @ SV122 )
| ( in @ SY535 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
| ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV122 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(881,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(882,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(883,plain,
! [SV43: $i,SV95: $i,SV111: $i,SV121: $i] :
( ( ( ! [SY534: $i] :
( ~ ( in @ SY534 @ SV121 )
| ( in @ SY534 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) ) )
= $true )
| ( ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV121 )
= $true )
| ( ( in @ SV121 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(884,plain,
! [SV43: $i,SV104: $i,SV106: $i] :
( ( ( in @ SV106 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $true )
| ( ( in @ SV104 @ ( sK40_SY509 @ SV106 @ SV104 @ SV43 ) )
= $true )
| ( ( SV104 = SV106 )
= $true )
| ( ( in @ SV104 @ SV43 )
= $false )
| ( ( in @ SV106 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(885,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
| ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(886,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(887,plain,
! [SV43: $i,SV95: $i,SV114: $i,SV122: $i] :
( ( ( ! [SY535: $i] :
( ~ ( in @ SY535 @ SV122 )
| ( in @ SY535 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) ) )
= $true )
| ( ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV122 )
= $true )
| ( ( in @ SV122 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(888,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(889,plain,
! [SV111: $i,SV95: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(890,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( ! [SY521: $i] :
~ ~ ( ~ ( in @ SY521 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SY521 @ SV95 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(891,plain,
! [SV43: $i,SV95: $i,SV111: $i,SV121: $i,SV123: $i] :
( ( ( ~ ( in @ SV123 @ SV121 )
| ( in @ SV123 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
= $true )
| ( ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV121 )
= $true )
| ( ( in @ SV121 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(892,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ~ ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(893,plain,
! [SV114: $i,SV95: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(894,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( ! [SY525: $i] :
~ ~ ( ~ ( in @ SY525 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SY525 @ SV95 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(895,plain,
! [SV43: $i,SV95: $i,SV114: $i,SV122: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV122 )
| ( in @ SV124 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
= $true )
| ( ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV122 )
= $true )
| ( ( in @ SV122 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(896,plain,
! [SV43: $i,SV95: $i,SV111: $i] :
( ( ( in @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(897,plain,
! [SV111: $i,SV95: $i,SV43: $i] :
( ( ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV95 )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(898,plain,
! [SV43: $i,SV95: $i,SV111: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ( in @ SV125 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SV125 @ SV95 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(899,plain,
! [SV43: $i,SV95: $i,SV111: $i,SV121: $i,SV123: $i] :
( ( ( ~ ( in @ SV123 @ SV121 ) )
= $true )
| ( ( in @ SV123 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
= $true )
| ( ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV121 )
= $true )
| ( ( in @ SV121 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(900,plain,
! [SV43: $i,SV95: $i,SV114: $i] :
( ( ( in @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) @ ( sK3_SY390 @ SV43 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(901,plain,
! [SV114: $i,SV95: $i,SV43: $i] :
( ( ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV95 )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(902,plain,
! [SV43: $i,SV95: $i,SV114: $i,SV126: $i] :
( ( ( ~ ~ ( ~ ( in @ SV126 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SV126 @ SV95 ) ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(903,plain,
! [SV43: $i,SV95: $i,SV114: $i,SV122: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV122 ) )
= $true )
| ( ( in @ SV124 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
= $true )
| ( ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV122 )
= $true )
| ( ( in @ SV122 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(904,plain,
! [SV43: $i,SV95: $i,SV111: $i,SV125: $i] :
( ( ( ~ ( ~ ( in @ SV125 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SV125 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(905,plain,
! [SV43: $i,SV95: $i,SV111: $i,SV121: $i,SV123: $i] :
( ( ( in @ SV123 @ SV121 )
= $false )
| ( ( in @ SV123 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
= $true )
| ( ( in @ ( sK41_SY520 @ SV43 @ SV95 @ SV111 ) @ SV121 )
= $true )
| ( ( in @ SV121 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(906,plain,
! [SV43: $i,SV95: $i,SV114: $i,SV126: $i] :
( ( ( ~ ( ~ ( in @ SV126 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SV126 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(907,plain,
! [SV43: $i,SV95: $i,SV114: $i,SV122: $i,SV124: $i] :
( ( ( in @ SV124 @ SV122 )
= $false )
| ( ( in @ SV124 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
= $true )
| ( ( in @ ( sK42_SY524 @ SV43 @ SV95 @ SV114 ) @ SV122 )
= $true )
| ( ( in @ SV122 @ ( sK3_SY390 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(908,plain,
! [SV43: $i,SV95: $i,SV111: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
| ~ ( in @ SV125 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(909,plain,
! [SV43: $i,SV95: $i,SV114: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
| ~ ( in @ SV126 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(910,plain,
! [SV43: $i,SV95: $i,SV111: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) ) )
= $true )
| ( ( ~ ( in @ SV125 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(911,plain,
! [SV43: $i,SV95: $i,SV114: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) ) )
= $true )
| ( ( ~ ( in @ SV126 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(912,plain,
! [SV43: $i,SV95: $i,SV111: $i,SV125: $i] :
( ( ( in @ SV125 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
= $false )
| ( ( ~ ( in @ SV125 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(913,plain,
! [SV43: $i,SV95: $i,SV114: $i,SV126: $i] :
( ( ( in @ SV126 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
= $false )
| ( ( ~ ( in @ SV126 @ SV95 ) )
= $true )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(914,plain,
! [SV43: $i,SV111: $i,SV95: $i,SV125: $i] :
( ( ( in @ SV125 @ SV95 )
= $false )
| ( ( in @ SV125 @ ( sK38_SY487 @ SV111 @ SV95 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV43 )
= $false )
| ( ( in @ SV111 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(915,plain,
! [SV43: $i,SV114: $i,SV95: $i,SV126: $i] :
( ( ( in @ SV126 @ SV95 )
= $false )
| ( ( in @ SV126 @ ( sK39_SY487 @ SV114 @ SV95 @ SV43 ) )
= $false )
| ( ( in @ ( sK31_SY485 @ SV43 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ SV114 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(916,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,915,914,907,905,901,900,897,896,884,877,876,874,867,864,862,861,852,851,816,809,786,781,780,779,773,772,767,766,763,751,736,728,713,686,676,675,669,650,649,648,639,630,629,627,626,624,623,613,611,610,607,600,599,596,593,589,582,581,576,573,567,566,556,555,554,549,537,536,535,532,531,523,521,520,518,517,515,512,511,497,471,470,469,442,432,416,415,412,409,403,385,384,383,381,380,370,354,350,349,346,320,318,317,316,314,309,297,290,280,279,278,266,241,191,190,189,143,142,141,94]) ).
thf(917,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[916]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU531^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:27:41 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.60/0.84
% 3.60/0.84 No.of.Axioms: 0
% 3.60/0.84
% 3.60/0.84 Length.of.Defs: 10142
% 3.60/0.84
% 3.60/0.84 Contains.Choice.Funs: true
% 3.60/0.84 ...................................
% 3.60/0.84
% 3.60/0.84 ********************************
% 3.60/0.84 * All subproblems solved! *
% 3.60/0.84 ********************************
% 3.60/0.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:47,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:916,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.60/0.84
% 3.60/0.84 %**** Beginning of derivation protocol ****
% 3.60/0.84 % SZS output start CNFRefutation
% See solution above
% 3.60/0.85
% 3.60/0.85 %**** End of derivation protocol ****
% 3.60/0.85 %**** no. of clauses in derivation: 917 ****
% 3.60/0.85 %**** clause counter: 916 ****
% 3.60/0.85
% 3.60/0.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:47,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:916,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------