%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU509^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 10:44:40 AM UTC 2026
% Result : Theorem 1.47s 0.48s
% Output : CNFRefutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 29
% Syntax : Number of formulae : 585 ( 229 unt; 0 typ; 28 def)
% Number of atoms : 4914 (1552 equ; 0 cnn)
% Maximal formula atoms : 27 ( 8 avg)
% Number of connectives : 12054 (2022 ~;1851 |; 122 &;7832 @)
% ( 21 <=>; 206 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 294 ( 294 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 30 con; 0-3 aty)
% Number of variables : 2101 ( 103 ^;1945 !; 53 ?;2101 :)
% 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_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $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_notinemptyset,type,
notinemptyset: $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_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK10_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_SY218,type,
sK12_SY218: $i > $i > $i > $i ).
thf(tp_sK13_SY205,type,
sK13_SY205: $i > $i > $i ).
thf(tp_sK14_SY219,type,
sK14_SY219: $i > $i > $i ).
thf(tp_sK15_Xx,type,
sK15_Xx: $i > $i > $i ).
thf(tp_sK16_SY54,type,
sK16_SY54: $i > ( $i > $o ) > $i ).
thf(tp_sK17_Xx,type,
sK17_Xx: ( $i > $o ) > $i ).
thf(tp_sK18_SY71,type,
sK18_SY71: $i > ( $i > $o ) > $i ).
thf(tp_sK19_Xx,type,
sK19_Xx: ( $i > $o ) > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK20_SY84,type,
sK20_SY84: $i > ( $i > $o ) > $i ).
thf(tp_sK21_Xx,type,
sK21_Xx: $i > $i > $i ).
thf(tp_sK22_Xx,type,
sK22_Xx: $i > $i > $i ).
thf(tp_sK23_Xx,type,
sK23_Xx: $i > $i ).
thf(tp_sK24_Xx,type,
sK24_Xx: $i > $i ).
thf(tp_sK2_Xx,type,
sK2_Xx: $i > $i > $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: $i > $i > $i ).
thf(tp_sK4_B,type,
sK4_B: $i > $i > $i ).
thf(tp_sK5_Xx,type,
sK5_Xx: $i > $i ).
thf(tp_sK6_B,type,
sK6_B: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK7_Xy,type,
sK7_Xy: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK8_SY21,type,
sK8_SY21: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK9_SY200,type,
sK9_SY200: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setbeta,type,
setbeta: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(prop2set,definition,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
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/sandbox/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
=> ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
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
=> ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
=> ( ! [SY19: $i > $i > $o,SY20: $i] :
( ! [SY21: $i] :
( ( in @ SY21 @ SY20 )
=> ? [SY23: $i] :
( ( SY19 @ SY21 @ SY23 )
& ! [SY24: $i] :
( ( SY19 @ SY21 @ SY24 )
=> ( SY23 = SY24 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY20 )
& ( SY19 @ 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 ) ) ) ) ) )
=> ( ! [SY51: $i > $o] :
( ? [SY53: $i] :
( ( SY51 @ SY53 )
& ! [SY54: $i] :
( ( SY51 @ SY54 )
=> ( SY53 = SY54 ) ) )
=> ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ 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 ) )
=> ( ! [SY68: $i > $o] :
( ? [SY70: $i] :
( ( SY68 @ SY70 )
& ! [SY71: $i] :
( ( SY68 @ SY71 )
=> ( SY70 = SY71 ) ) )
=> ? [Xx: $i] :
( ( SY68 @ Xx )
& ! [Xy: $i] :
( ( SY68 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY74: $o,SY75: $i] :
( ( in @ SY75
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY76: $i] : SY74 ) )
=> SY74 )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY81: $i > $o] :
( ? [SY83: $i] :
( ( SY81 @ SY83 )
& ! [SY84: $i] :
( ( SY81 @ SY84 )
=> ( SY83 = SY84 ) ) )
=> ? [Xx: $i] : ( SY81 @ 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 ) ) )
=> ! [SY0: $i] :
( ( SY0 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,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,
( ( ! [SY19: $i > $i > $o,SY20: $i] :
( ! [SY21: $i] :
( ( in @ SY21 @ SY20 )
=> ? [SY23: $i] :
( ( SY19 @ SY21 @ SY23 )
& ! [SY24: $i] :
( ( SY19 @ SY21 @ SY24 )
=> ( SY23 = SY24 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY20 )
& ( SY19 @ 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,
( ( ! [SY51: $i > $o] :
( ? [SY53: $i] :
( ( SY51 @ SY53 )
& ! [SY54: $i] :
( ( SY51 @ SY54 )
=> ( SY53 = SY54 ) ) )
=> ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ 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,
( ( ! [SY68: $i > $o] :
( ? [SY70: $i] :
( ( SY68 @ SY70 )
& ! [SY71: $i] :
( ( SY68 @ SY71 )
=> ( SY70 = SY71 ) ) )
=> ? [Xx: $i] :
( ( SY68 @ Xx )
& ! [Xy: $i] :
( ( SY68 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [SY74: $o,SY75: $i] :
( ( in @ SY75
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY76: $i] : SY74 ) )
=> SY74 ) )
= $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,
( ( ! [SY81: $i > $o] :
( ? [SY83: $i] :
( ( SY81 @ SY83 )
& ! [SY84: $i] :
( ( SY81 @ SY84 )
=> ( SY83 = SY84 ) ) )
=> ? [Xx: $i] : ( SY81 @ 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,
( ( ! [SY0: $i] :
( ( SY0 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY0 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ~ ! [SY0: $i] :
( ( SY0 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(31,plain,
( ( ( sK1_SY0 != emptyset )
& ! [SY194: $i] :
~ ( in @ SY194 @ sK1_SY0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK2_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK2_Xx @ B @ A ) @ A )
| ( in @ ( sK2_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(33,plain,
( ( ! [Xx: $i] :
( ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) )
& ! [A: $i,Xy: $i] :
( ( Xy != Xx )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
& ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK3_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(35,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK4_B @ Xx @ A ) )
& ( in @ ( sK4_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(36,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK5_Xx @ A ) @ omega )
& ( in @ ( sK5_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK5_Xx @ A ) @ ( sK5_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(38,plain,
( ( ! [SY19: $i > $i > $o,SY20: $i] :
( ( ( in @ ( sK8_SY21 @ SY20 @ SY19 ) @ SY20 )
& ! [SY199: $i] :
( ( ( SY19 @ ( sK8_SY21 @ SY20 @ SY19 ) @ ( sK9_SY200 @ SY199 @ SY20 @ SY19 ) )
& ( SY199
!= ( sK9_SY200 @ SY199 @ SY20 @ SY19 ) ) )
| ~ ( SY19 @ ( sK8_SY21 @ SY20 @ SY19 ) @ SY199 ) ) )
| ( ! [SY195: $i] :
( ! [Xy: $i] :
( ~ ( SY19 @ Xy @ SY195 )
| ~ ( in @ Xy @ SY20 ) )
| ( in @ SY195 @ ( sK6_B @ SY20 @ SY19 ) ) )
& ! [SY197: $i] :
( ~ ( in @ SY197 @ ( sK6_B @ SY20 @ SY19 ) )
| ( ( SY19 @ ( sK7_Xy @ SY197 @ SY20 @ SY19 ) @ SY197 )
& ( in @ ( sK7_Xy @ SY197 @ SY20 @ SY19 ) @ SY20 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(39,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK10_B @ A ) @ A )
& ! [SY201: $i] :
( ~ ( in @ SY201 @ ( sK10_B @ A ) )
| ~ ( in @ SY201 @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(40,plain,
( ( ! [A: $i] :
( ! [SY202: $i] :
( ( ( in @ ( sK15_Xx @ SY202 @ A ) @ SY202 )
& ~ ( in @ ( sK15_Xx @ SY202 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY202 )
| ( ! [SY223: $i] :
( ~ ( in @ SY223 @ ( sK11_B @ A ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY223 )
| ( in @ SY221 @ ( sK13_SY205 @ SY202 @ A ) ) )
| ( in @ ( sK14_SY219 @ SY202 @ A ) @ SY223 ) )
& ( in @ ( sK13_SY205 @ SY202 @ A ) @ ( sK11_B @ A ) )
& ( in @ ( sK14_SY219 @ SY202 @ A ) @ SY202 )
& ! [SY222: $i] :
( ~ ( in @ SY222 @ ( sK13_SY205 @ SY202 @ A ) )
| ~ ( in @ SY222 @ SY202 ) ) ) )
& ! [SY210: $i,SY211: $i] :
( ~ ( in @ SY210 @ ( sK11_B @ A ) )
| ~ ( in @ SY211 @ ( sK11_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY210 )
| ( in @ Xx @ SY211 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY211 )
| ( in @ Xx @ SY210 ) ) )
& ! [SY214: $i] :
( ~ ( in @ SY214 @ ( sK11_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY214 )
| ( in @ Xx @ A ) ) )
& ! [SY216: $i,SY217: $i] :
( ~ ( in @ SY216 @ A )
| ~ ( in @ SY217 @ A )
| ( ( in @ ( sK12_SY218 @ SY217 @ SY216 @ A ) @ ( sK11_B @ A ) )
& ( ~ ( in @ SY216 @ ( sK12_SY218 @ SY217 @ SY216 @ A ) )
| ~ ( in @ SY217 @ ( sK12_SY218 @ SY217 @ SY216 @ A ) ) )
& ( ( in @ SY216 @ ( sK12_SY218 @ SY217 @ SY216 @ A ) )
| ( in @ SY217 @ ( sK12_SY218 @ SY217 @ SY216 @ A ) ) ) )
| ( SY216 = SY217 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(41,plain,
( ( ! [SY51: $i > $o] :
( ! [SY53: $i] :
( ( ( SY51 @ ( sK16_SY54 @ SY53 @ SY51 ) )
& ( SY53
!= ( sK16_SY54 @ SY53 @ SY51 ) ) )
| ~ ( SY51 @ SY53 ) )
| ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(42,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(43,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(44,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(45,plain,
( ( ! [SY68: $i > $o] :
( ! [SY70: $i] :
( ( ( SY68 @ ( sK18_SY71 @ SY70 @ SY68 ) )
& ( SY70
!= ( sK18_SY71 @ SY70 @ SY68 ) ) )
| ~ ( SY68 @ SY70 ) )
| ( ! [SY226: $i] :
( ~ ( SY68 @ SY226 )
| ( ( sK17_Xx @ SY68 )
= SY226 ) )
& ( SY68 @ ( sK17_Xx @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(46,plain,
( ( ! [SY74: $o] :
( ! [SY75: $i] :
~ ( in @ SY75
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY76: $i] : SY74 ) )
| SY74 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(47,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(48,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(49,plain,
( ( ! [SY81: $i > $o] :
( ! [SY83: $i] :
( ( ( SY81 @ ( sK20_SY84 @ SY83 @ SY81 ) )
& ( SY83
!= ( sK20_SY84 @ SY83 @ SY81 ) ) )
| ~ ( SY81 @ SY83 ) )
| ( SY81 @ ( sK19_Xx @ SY81 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK22_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK22_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK21_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK21_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( in @ ( sK23_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( in @ ( sK24_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(53,plain,
( ( ! [A: $i] :
( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
& ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(54,plain,
( ( ! [A: $i] :
( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
& ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( in @ ( sK24_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( in @ ( sK23_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK22_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK22_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK21_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK21_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(58,plain,
( ( ! [SY81: $i > $o] :
( ! [SY83: $i] :
( ( ( SY81 @ ( sK20_SY84 @ SY83 @ SY81 ) )
& ( SY83
!= ( sK20_SY84 @ SY83 @ SY81 ) ) )
| ~ ( SY81 @ SY83 ) )
| ( SY81 @ ( sK19_Xx @ SY81 ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(59,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(60,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(61,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(62,plain,
( ( ! [SY74: $o] :
( ! [SY75: $i] :
~ ( in @ SY75
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY76: $i] : SY74 ) )
| SY74 ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(63,plain,
( ( ! [SY68: $i > $o] :
( ! [SY70: $i] :
( ( ( SY68 @ ( sK18_SY71 @ SY70 @ SY68 ) )
& ( SY70
!= ( sK18_SY71 @ SY70 @ SY68 ) ) )
| ~ ( SY68 @ SY70 ) )
| ( ! [SY226: $i] :
( ~ ( SY68 @ SY226 )
| ( ( sK17_Xx @ SY68 )
= SY226 ) )
& ( SY68 @ ( sK17_Xx @ SY68 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(64,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(65,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(66,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)],[42]) ).
thf(67,plain,
( ( ! [SY51: $i > $o] :
( ! [SY53: $i] :
( ( ( SY51 @ ( sK16_SY54 @ SY53 @ SY51 ) )
& ( SY53
!= ( sK16_SY54 @ SY53 @ SY51 ) ) )
| ~ ( SY51 @ SY53 ) )
| ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(68,plain,
( ( ! [A: $i] :
( ! [SY202: $i] :
( ( ( in @ ( sK15_Xx @ SY202 @ A ) @ SY202 )
& ~ ( in @ ( sK15_Xx @ SY202 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY202 )
| ( ! [SY223: $i] :
( ~ ( in @ SY223 @ ( sK11_B @ A ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY223 )
| ( in @ SY221 @ ( sK13_SY205 @ SY202 @ A ) ) )
| ( in @ ( sK14_SY219 @ SY202 @ A ) @ SY223 ) )
& ( in @ ( sK13_SY205 @ SY202 @ A ) @ ( sK11_B @ A ) )
& ( in @ ( sK14_SY219 @ SY202 @ A ) @ SY202 )
& ! [SY222: $i] :
( ~ ( in @ SY222 @ ( sK13_SY205 @ SY202 @ A ) )
| ~ ( in @ SY222 @ SY202 ) ) ) )
& ! [SY210: $i,SY211: $i] :
( ~ ( in @ SY210 @ ( sK11_B @ A ) )
| ~ ( in @ SY211 @ ( sK11_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY210 )
| ( in @ Xx @ SY211 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY211 )
| ( in @ Xx @ SY210 ) ) )
& ! [SY214: $i] :
( ~ ( in @ SY214 @ ( sK11_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY214 )
| ( in @ Xx @ A ) ) )
& ! [SY216: $i,SY217: $i] :
( ~ ( in @ SY216 @ A )
| ~ ( in @ SY217 @ A )
| ( ( in @ ( sK12_SY218 @ SY217 @ SY216 @ A ) @ ( sK11_B @ A ) )
& ( ~ ( in @ SY216 @ ( sK12_SY218 @ SY217 @ SY216 @ A ) )
| ~ ( in @ SY217 @ ( sK12_SY218 @ SY217 @ SY216 @ A ) ) )
& ( ( in @ SY216 @ ( sK12_SY218 @ SY217 @ SY216 @ A ) )
| ( in @ SY217 @ ( sK12_SY218 @ SY217 @ SY216 @ A ) ) ) )
| ( SY216 = SY217 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(69,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK10_B @ A ) @ A )
& ! [SY201: $i] :
( ~ ( in @ SY201 @ ( sK10_B @ A ) )
| ~ ( in @ SY201 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(70,plain,
( ( ! [SY19: $i > $i > $o,SY20: $i] :
( ( ( in @ ( sK8_SY21 @ SY20 @ SY19 ) @ SY20 )
& ! [SY199: $i] :
( ( ( SY19 @ ( sK8_SY21 @ SY20 @ SY19 ) @ ( sK9_SY200 @ SY199 @ SY20 @ SY19 ) )
& ( SY199
!= ( sK9_SY200 @ SY199 @ SY20 @ SY19 ) ) )
| ~ ( SY19 @ ( sK8_SY21 @ SY20 @ SY19 ) @ SY199 ) ) )
| ( ! [SY195: $i] :
( ! [Xy: $i] :
( ~ ( SY19 @ Xy @ SY195 )
| ~ ( in @ Xy @ SY20 ) )
| ( in @ SY195 @ ( sK6_B @ SY20 @ SY19 ) ) )
& ! [SY197: $i] :
( ~ ( in @ SY197 @ ( sK6_B @ SY20 @ SY19 ) )
| ( ( SY19 @ ( sK7_Xy @ SY197 @ SY20 @ SY19 ) @ SY197 )
& ( in @ ( sK7_Xy @ SY197 @ SY20 @ SY19 ) @ SY20 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(71,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK5_Xx @ A ) @ omega )
& ( in @ ( sK5_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK5_Xx @ A ) @ ( sK5_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(72,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(73,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(74,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK4_B @ Xx @ A ) )
& ( in @ ( sK4_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK3_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(76,plain,
( ( ! [Xx: $i] :
( ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) )
& ! [A: $i,Xy: $i] :
( ( Xy != Xx )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
& ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(77,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK2_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK2_Xx @ B @ A ) @ A )
| ( in @ ( sK2_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(79,plain,
( ( ( sK1_SY0 != emptyset )
& ! [SY194: $i] :
~ ( in @ SY194 @ sK1_SY0 ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SX0 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SX0 ) @ ( sK5_Xx @ SX0 ) ) @ SX0 ) )
| ~ ( in @ emptyset @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(81,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(82,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK4_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_B @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(83,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK20_SY84 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK20_SY84 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ ( sK19_Xx @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(84,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK16_SY54 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK16_SY54 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(85,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK18_SY71 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK18_SY71 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK17_Xx @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK17_Xx @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(86,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK15_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK11_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( sK13_SY205 @ SX1 @ SX0 ) ) )
| ( in @ ( sK14_SY219 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SX1 @ SX0 ) @ ( sK11_B @ SX0 ) )
| ~ ( in @ ( sK14_SY219 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK13_SY205 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK11_B @ SX0 ) )
| ~ ( in @ SX2 @ ( sK11_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK11_B @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SX2 @ SX1 @ SX0 ) @ ( sK11_B @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ SX1 @ ( sK12_SY218 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK12_SY218 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( in @ SX1 @ ( sK12_SY218 @ SX2 @ SX1 @ SX0 ) )
| ( in @ SX2 @ ( sK12_SY218 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK22_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK22_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( in @ ( sK21_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK21_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(88,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(89,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_SY21 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK8_SY21 @ SX1 @ SX0 ) @ ( sK9_SY200 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK9_SY200 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ ( sK8_SY21 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( SX0 @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX2 @ ( sK6_B @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK6_B @ SX1 @ SX0 ) )
| ~ ( ~ ( SX0 @ ( sK7_Xy @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK7_Xy @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(91,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
| ~ ! [SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(92,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ ( sK10_B @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK10_B @ SX0 ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(93,plain,
( ( ~ ( ~ ( ( sK1_SY0 != emptyset ) )
| ~ ! [SX0: $i] :
~ ( in @ SX0 @ sK1_SY0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setbeta,setext,setextAx,setunionAx,wellorderingAx]) ).
thf(94,plain,
! [SV1: $i] :
( ( ( in @ ( sK24_Xx @ SV1 ) @ SV1 )
| ( SV1 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(95,plain,
! [SV2: $i] :
( ( ( in @ ( sK23_Xx @ SV2 ) @ SV2 )
| ( SV2 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(96,plain,
! [SV3: $i] :
( ( ~ ( in @ SV3 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(97,plain,
! [SV4: $i] :
( ( ~ ( in @ SV4 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(98,plain,
( ( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(99,plain,
! [SV5: $o] :
( ( ! [SY227: $i] :
~ ( in @ SY227
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY228: $i] : SV5 ) )
| SV5 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[62]) ).
thf(100,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[62]) ).
thf(101,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[62]) ).
thf(102,plain,
! [SV6: $i] :
( ( ! [SY229: $i > $o,SY230: $i] :
( ~ ( in @ SY230
@ ( dsetconstr @ SV6
@ ^ [Xy: $i] : ( SY229 @ Xy ) ) )
| ( SY229 @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(103,plain,
! [SV7: $i] :
( ( ! [SY232: $i > $o,SY233: $i] :
( ~ ( in @ SY233
@ ( dsetconstr @ SV7
@ ^ [Xy: $i] : ( SY232 @ Xy ) ) )
| ( in @ SY233 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(104,plain,
! [SV8: $i] :
( ( ! [SY235: $i > $o,SY236: $i] :
( ~ ( in @ SY236 @ SV8 )
| ~ ( SY235 @ SY236 )
| ( in @ SY236
@ ( dsetconstr @ SV8
@ ^ [Xy: $i] : ( SY235 @ Xy ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(105,plain,
! [SV9: $i] :
( ( ~ ( in @ SV9 @ omega )
| ( in @ ( setadjoin @ SV9 @ SV9 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(106,plain,
! [SV10: $i] :
( ( ~ ( in @ SV10 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(107,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV11 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV11 ) @ SV11 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 ) )
| ~ ( in @ emptyset @ SV11 )
| ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(108,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(109,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK4_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(110,plain,
! [SV12: $i > $o] :
( ( ! [SY239: $i] :
( ~ ( ~ ( SV12 @ ( sK20_SY84 @ SY239 @ SV12 ) )
| ~ ( ( SY239
!= ( sK20_SY84 @ SY239 @ SV12 ) ) ) )
| ~ ( SV12 @ SY239 ) )
| ( SV12 @ ( sK19_Xx @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(111,plain,
! [SV13: $i > $o] :
( ( ! [SY240: $i] :
( ~ ( ~ ( SV13 @ ( sK16_SY54 @ SY240 @ SV13 ) )
| ~ ( ( SY240
!= ( sK16_SY54 @ SY240 @ SV13 ) ) ) )
| ~ ( SV13 @ SY240 ) )
| ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(112,plain,
! [SV14: $i > $o] :
( ( ! [SY242: $i] :
( ~ ( ~ ( SV14 @ ( sK18_SY71 @ SY242 @ SV14 ) )
| ~ ( ( SY242
!= ( sK18_SY71 @ SY242 @ SV14 ) ) ) )
| ~ ( SV14 @ SY242 ) )
| ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(113,plain,
! [SV15: $i] :
( ( ~ ( ~ ! [SY244: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SY244 @ SV15 ) @ SY244 )
| ~ ~ ( in @ ( sK15_Xx @ SY244 @ SV15 ) @ SV15 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY244 )
| ~ ( ~ ! [SY246: $i] :
( ~ ( in @ SY246 @ ( sK11_B @ SV15 ) )
| ! [SY247: $i] :
( ~ ( in @ SY247 @ SY246 )
| ( in @ SY247 @ ( sK13_SY205 @ SY244 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SY244 @ SV15 ) @ SY246 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SY244 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SY244 @ SV15 ) @ SY244 ) )
| ~ ! [SY248: $i] :
( ~ ( in @ SY248 @ ( sK13_SY205 @ SY244 @ SV15 ) )
| ~ ( in @ SY248 @ SY244 ) ) ) ) )
| ~ ~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SY250 @ ( sK11_B @ SV15 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(114,plain,
! [SV16: $i] :
( ( ! [SY257: $i] :
( ~ ( ~ ( in @ ( sK22_Xx @ SY257 @ SV16 ) @ SV16 )
| ~ ~ ( in @ ( sK22_Xx @ SY257 @ SV16 ) @ SY257 ) )
| ~ ( ~ ( in @ ( sK21_Xx @ SY257 @ SV16 ) @ SY257 )
| ~ ~ ( in @ ( sK21_Xx @ SY257 @ SV16 ) @ SV16 ) )
| ( SV16 = SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(115,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( in @ SY259 @ ( setadjoin @ SV17 @ SY258 ) )
| ( SY259 = SV17 )
| ( in @ SY259 @ SY258 ) )
| ~ ~ ( ~ ! [SY260: $i,SY261: $i] :
( ( SY261 != SV17 )
| ( in @ SY261 @ ( setadjoin @ SV17 @ SY260 ) ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( in @ SY263 @ SY262 )
| ( in @ SY263 @ ( setadjoin @ SV17 @ SY262 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(116,plain,
! [SV18: $i > $i > $o] :
( ( ! [SY264: $i] :
( ~ ( ~ ( in @ ( sK8_SY21 @ SY264 @ SV18 ) @ SY264 )
| ~ ! [SY265: $i] :
( ~ ( ~ ( SV18 @ ( sK8_SY21 @ SY264 @ SV18 ) @ ( sK9_SY200 @ SY265 @ SY264 @ SV18 ) )
| ~ ( ( SY265
!= ( sK9_SY200 @ SY265 @ SY264 @ SV18 ) ) ) )
| ~ ( SV18 @ ( sK8_SY21 @ SY264 @ SV18 ) @ SY265 ) ) )
| ~ ( ~ ! [SY266: $i] :
( ! [SY267: $i] :
( ~ ( SV18 @ SY267 @ SY266 )
| ~ ( in @ SY267 @ SY264 ) )
| ( in @ SY266 @ ( sK6_B @ SY264 @ SV18 ) ) )
| ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ ( sK6_B @ SY264 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY268 @ SY264 @ SV18 ) @ SY268 )
| ~ ( in @ ( sK7_Xy @ SY268 @ SY264 @ SV18 ) @ SY264 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(117,plain,
! [SV19: $i] :
( ( ! [SY269: $i] :
( ~ ( ~ ( ~ ( in @ ( sK2_Xx @ SY269 @ SV19 ) @ SV19 )
| ~ ( in @ ( sK2_Xx @ SY269 @ SV19 ) @ SY269 ) )
| ~ ( ( in @ ( sK2_Xx @ SY269 @ SV19 ) @ SV19 )
| ( in @ ( sK2_Xx @ SY269 @ SV19 ) @ SY269 ) ) )
| ( SV19 = SY269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(118,plain,
! [SV20: $i] :
( ( ~ ( ~ ! [SY270: $i > $o,SY271: $i] :
( ~ ( in @ SY271 @ SV20 )
| ~ ( SY270 @ SY271 )
| ( in @ SY271
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY270 @ SX3 ) ) ) )
| ~ ! [SY273: $i > $o,SY274: $i] :
( ~ ( in @ SY274 @ SV20 )
| ~ ( in @ SY274
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY273 @ SX3 ) ) )
| ( SY273 @ SY274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(119,plain,
! [SV21: $i] :
( ( ! [SY276: $i] :
~ ( in @ SY276 @ SV21 )
| ~ ( ~ ( in @ ( sK10_B @ SV21 ) @ SV21 )
| ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ ( sK10_B @ SV21 ) )
| ~ ( in @ SY277 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(120,plain,
( ( ~ ( ( sK1_SY0 != emptyset ) )
| ~ ! [SX0: $i] :
~ ( in @ SX0 @ sK1_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(121,plain,
! [SV1: $i] :
( ( ( in @ ( sK24_Xx @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(122,plain,
! [SV2: $i] :
( ( ( in @ ( sK23_Xx @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(123,plain,
! [SV3: $i] :
( ( in @ SV3 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(124,plain,
! [SV4: $i] :
( ( in @ SV4 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(125,plain,
! [SV22: $i] :
( ( ( ~ ( in @ SV22 @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(126,plain,
! [SV5: $o] :
( ( ( ! [SY227: $i] :
~ ( in @ SY227
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY228: $i] : SV5 ) ) )
= $true )
| ( SV5 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(127,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(128,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(129,plain,
! [SV23: $i > $o,SV6: $i] :
( ( ! [SY278: $i] :
( ~ ( in @ SY278
@ ( dsetconstr @ SV6
@ ^ [SY279: $i] : ( SV23 @ SY279 ) ) )
| ( SV23 @ SY278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(130,plain,
! [SV24: $i > $o,SV7: $i] :
( ( ! [SY280: $i] :
( ~ ( in @ SY280
@ ( dsetconstr @ SV7
@ ^ [SY281: $i] : ( SV24 @ SY281 ) ) )
| ( in @ SY280 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(131,plain,
! [SV25: $i > $o,SV8: $i] :
( ( ! [SY282: $i] :
( ~ ( in @ SY282 @ SV8 )
| ~ ( SV25 @ SY282 )
| ( in @ SY282
@ ( dsetconstr @ SV8
@ ^ [SY283: $i] : ( SV25 @ SY283 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(132,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV9 @ SV9 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(133,plain,
! [SV10: $i] :
( ( in @ SV10 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(134,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV11 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV11 ) @ SV11 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 ) )
| ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(135,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(136,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(137,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(138,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK4_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(139,plain,
! [SV12: $i > $o] :
( ( ( ! [SY239: $i] :
( ~ ( ~ ( SV12 @ ( sK20_SY84 @ SY239 @ SV12 ) )
| ~ ( ( SY239
!= ( sK20_SY84 @ SY239 @ SV12 ) ) ) )
| ~ ( SV12 @ SY239 ) ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(140,plain,
! [SV13: $i > $o] :
( ( ( ! [SY240: $i] :
( ~ ( ~ ( SV13 @ ( sK16_SY54 @ SY240 @ SV13 ) )
| ~ ( ( SY240
!= ( sK16_SY54 @ SY240 @ SV13 ) ) ) )
| ~ ( SV13 @ SY240 ) ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(141,plain,
! [SV14: $i > $o] :
( ( ( ! [SY242: $i] :
( ~ ( ~ ( SV14 @ ( sK18_SY71 @ SY242 @ SV14 ) )
| ~ ( ( SY242
!= ( sK18_SY71 @ SY242 @ SV14 ) ) ) )
| ~ ( SV14 @ SY242 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(142,plain,
! [SV15: $i] :
( ( ~ ! [SY244: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SY244 @ SV15 ) @ SY244 )
| ~ ~ ( in @ ( sK15_Xx @ SY244 @ SV15 ) @ SV15 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY244 )
| ~ ( ~ ! [SY246: $i] :
( ~ ( in @ SY246 @ ( sK11_B @ SV15 ) )
| ! [SY247: $i] :
( ~ ( in @ SY247 @ SY246 )
| ( in @ SY247 @ ( sK13_SY205 @ SY244 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SY244 @ SV15 ) @ SY246 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SY244 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SY244 @ SV15 ) @ SY244 ) )
| ~ ! [SY248: $i] :
( ~ ( in @ SY248 @ ( sK13_SY205 @ SY244 @ SV15 ) )
| ~ ( in @ SY248 @ SY244 ) ) ) ) )
| ~ ~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SY250 @ ( sK11_B @ SV15 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(143,plain,
! [SV16: $i,SV26: $i] :
( ( ~ ( ~ ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
| ~ ~ ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 ) )
| ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
| ( SV16 = SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(144,plain,
! [SV17: $i] :
( ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( in @ SY259 @ ( setadjoin @ SV17 @ SY258 ) )
| ( SY259 = SV17 )
| ( in @ SY259 @ SY258 ) )
| ~ ~ ( ~ ! [SY260: $i,SY261: $i] :
( ( SY261 != SV17 )
| ( in @ SY261 @ ( setadjoin @ SV17 @ SY260 ) ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( in @ SY263 @ SY262 )
| ( in @ SY263 @ ( setadjoin @ SV17 @ SY262 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(145,plain,
! [SV18: $i > $i > $o,SV27: $i] :
( ( ~ ( ~ ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
| ~ ! [SY284: $i] :
( ~ ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) )
| ~ ( ( SY284
!= ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) ) ) )
| ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SY284 ) ) )
| ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(146,plain,
! [SV19: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) )
| ~ ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) ) )
| ( SV19 = SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(147,plain,
! [SV20: $i] :
( ( ~ ! [SY270: $i > $o,SY271: $i] :
( ~ ( in @ SY271 @ SV20 )
| ~ ( SY270 @ SY271 )
| ( in @ SY271
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY270 @ SX3 ) ) ) )
| ~ ! [SY273: $i > $o,SY274: $i] :
( ~ ( in @ SY274 @ SV20 )
| ~ ( in @ SY274
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY273 @ SX3 ) ) )
| ( SY273 @ SY274 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(148,plain,
! [SV21: $i] :
( ( ( ! [SY276: $i] :
~ ( in @ SY276 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK10_B @ SV21 ) @ SV21 )
| ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ ( sK10_B @ SV21 ) )
| ~ ( in @ SY277 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(149,plain,
( ( ~ ( ( sK1_SY0 != emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(150,plain,
( ( ~ ! [SX0: $i] :
~ ( in @ SX0 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(151,plain,
! [SV22: $i] :
( ( ( in @ SV22 @ emptyset )
= $false )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(152,plain,
! [SV5: $o,SV29: $i] :
( ( ( ~ ( in @ SV29
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY228: $i] : SV5 ) ) )
= $true )
| ( SV5 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(153,plain,
! [SV30: $i] :
( ( ( ~ ( in @ SV30
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(154,plain,
! [SV31: $i] :
( ( ( ~ ( in @ SV31
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(155,plain,
! [SV23: $i > $o,SV6: $i,SV32: $i] :
( ( ~ ( in @ SV32
@ ( dsetconstr @ SV6
@ ^ [SY279: $i] : ( SV23 @ SY279 ) ) )
| ( SV23 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(156,plain,
! [SV24: $i > $o,SV7: $i,SV33: $i] :
( ( ~ ( in @ SV33
@ ( dsetconstr @ SV7
@ ^ [SY281: $i] : ( SV24 @ SY281 ) ) )
| ( in @ SV33 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(157,plain,
! [SV25: $i > $o,SV8: $i,SV34: $i] :
( ( ~ ( in @ SV34 @ SV8 )
| ~ ( SV25 @ SV34 )
| ( in @ SV34
@ ( dsetconstr @ SV8
@ ^ [SY283: $i] : ( SV25 @ SY283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(158,plain,
! [SV9: $i] :
( ( ( in @ SV9 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV9 @ SV9 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(159,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV11 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV11 ) @ SV11 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(160,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(161,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(162,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK4_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(164,plain,
! [SV35: $i,SV12: $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK20_SY84 @ SV35 @ SV12 ) )
| ~ ( ( SV35
!= ( sK20_SY84 @ SV35 @ SV12 ) ) ) )
| ~ ( SV12 @ SV35 ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(165,plain,
! [SV36: $i,SV13: $i > $o] :
( ( ( ~ ( ~ ( SV13 @ ( sK16_SY54 @ SV36 @ SV13 ) )
| ~ ( ( SV36
!= ( sK16_SY54 @ SV36 @ SV13 ) ) ) )
| ~ ( SV13 @ SV36 ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(166,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ( ~ ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
| ~ ( ( SV37
!= ( sK18_SY71 @ SV37 @ SV14 ) ) ) )
| ~ ( SV14 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(167,plain,
! [SV15: $i] :
( ( ~ ! [SY244: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SY244 @ SV15 ) @ SY244 )
| ~ ~ ( in @ ( sK15_Xx @ SY244 @ SV15 ) @ SV15 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY244 )
| ~ ( ~ ! [SY246: $i] :
( ~ ( in @ SY246 @ ( sK11_B @ SV15 ) )
| ! [SY247: $i] :
( ~ ( in @ SY247 @ SY246 )
| ( in @ SY247 @ ( sK13_SY205 @ SY244 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SY244 @ SV15 ) @ SY246 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SY244 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SY244 @ SV15 ) @ SY244 ) )
| ~ ! [SY248: $i] :
( ~ ( in @ SY248 @ ( sK13_SY205 @ SY244 @ SV15 ) )
| ~ ( in @ SY248 @ SY244 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(168,plain,
! [SV15: $i] :
( ( ~ ~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SY250 @ ( sK11_B @ SV15 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(169,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
| ~ ~ ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
| ( SV16 = SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(170,plain,
! [SV17: $i] :
( ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( in @ SY259 @ ( setadjoin @ SV17 @ SY258 ) )
| ( SY259 = SV17 )
| ( in @ SY259 @ SY258 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(171,plain,
! [SV17: $i] :
( ( ~ ~ ( ~ ! [SY260: $i,SY261: $i] :
( ( SY261 != SV17 )
| ( in @ SY261 @ ( setadjoin @ SV17 @ SY260 ) ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( in @ SY263 @ SY262 )
| ( in @ SY263 @ ( setadjoin @ SV17 @ SY262 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(172,plain,
! [SV18: $i > $i > $o,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
| ~ ! [SY284: $i] :
( ~ ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) )
| ~ ( ( SY284
!= ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) ) ) )
| ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SY284 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(173,plain,
! [SV19: $i,SV28: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) )
| ~ ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) ) ) )
= $true )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(174,plain,
! [SV20: $i] :
( ( ~ ! [SY270: $i > $o,SY271: $i] :
( ~ ( in @ SY271 @ SV20 )
| ~ ( SY270 @ SY271 )
| ( in @ SY271
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY270 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(175,plain,
! [SV20: $i] :
( ( ~ ! [SY273: $i > $o,SY274: $i] :
( ~ ( in @ SY274 @ SV20 )
| ~ ( in @ SY274
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY273 @ SX3 ) ) )
| ( SY273 @ SY274 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(176,plain,
! [SV21: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK10_B @ SV21 ) @ SV21 )
| ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ ( sK10_B @ SV21 ) )
| ~ ( in @ SY277 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(177,plain,
( ( sK1_SY0 != emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(178,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ sK1_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(179,plain,
! [SV22: $i,SV39: $o] :
( ( SV39 = $true )
| ( ( in @ SV22 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[151]) ).
thf(180,plain,
! [SV22: $i] :
( ( $true = $true )
| ( ( in @ SV22 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[151]) ).
thf(181,plain,
! [SV22: $i] :
( ( $false = $true )
| ( ( in @ SV22 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[151]) ).
thf(182,plain,
! [SV5: $o,SV29: $i] :
( ( ( in @ SV29
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY228: $i] : SV5 ) )
= $false )
| ( SV5 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(183,plain,
! [SV30: $i] :
( ( ( in @ SV30
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(184,plain,
! [SV31: $i] :
( ( ( in @ SV31
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(185,plain,
! [SV23: $i > $o,SV6: $i,SV32: $i] :
( ( ( ~ ( in @ SV32
@ ( dsetconstr @ SV6
@ ^ [SY279: $i] : ( SV23 @ SY279 ) ) ) )
= $true )
| ( ( SV23 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(186,plain,
! [SV24: $i > $o,SV7: $i,SV33: $i] :
( ( ( ~ ( in @ SV33
@ ( dsetconstr @ SV7
@ ^ [SY281: $i] : ( SV24 @ SY281 ) ) ) )
= $true )
| ( ( in @ SV33 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(187,plain,
! [SV25: $i > $o,SV8: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ SV8 ) )
= $true )
| ( ( ~ ( SV25 @ SV34 )
| ( in @ SV34
@ ( dsetconstr @ SV8
@ ^ [SY283: $i] : ( SV25 @ SY283 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(188,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV11 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV11 ) @ SV11 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(189,plain,
! [SV40: $i] :
( ( ! [SY294: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SY294 @ SV40 ) @ SY294 )
| ~ ~ ( in @ ( sK3_Xx @ SY294 @ SV40 ) @ SV40 ) )
| ( in @ SY294 @ ( powerset @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(190,plain,
! [SV41: $i] :
( ( ! [SY295: $i] :
( ~ ( in @ SY295 @ ( powerset @ SV41 ) )
| ! [SY296: $i] :
( ~ ( in @ SY296 @ SY295 )
| ( in @ SY296 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(191,plain,
! [SV42: $i] :
( ( ! [SY297: $i] :
( ! [SY298: $i] :
( ~ ( in @ SY297 @ SY298 )
| ~ ( in @ SY298 @ SV42 ) )
| ( in @ SY297 @ ( setunion @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(192,plain,
! [SV43: $i] :
( ( ! [SY299: $i] :
( ~ ( in @ SY299 @ ( setunion @ SV43 ) )
| ~ ( ~ ( in @ SY299 @ ( sK4_B @ SY299 @ SV43 ) )
| ~ ( in @ ( sK4_B @ SY299 @ SV43 ) @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(193,plain,
! [SV35: $i,SV12: $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK20_SY84 @ SV35 @ SV12 ) )
| ~ ( ( SV35
!= ( sK20_SY84 @ SV35 @ SV12 ) ) ) ) )
= $true )
| ( ( ~ ( SV12 @ SV35 ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(194,plain,
! [SV36: $i,SV13: $i > $o] :
( ( ( ~ ( ~ ( SV13 @ ( sK16_SY54 @ SV36 @ SV13 ) )
| ~ ( ( SV36
!= ( sK16_SY54 @ SV36 @ SV13 ) ) ) ) )
= $true )
| ( ( ~ ( SV13 @ SV36 ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(195,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ( ~ ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
| ~ ( ( SV37
!= ( sK18_SY71 @ SV37 @ SV14 ) ) ) ) )
= $true )
| ( ( ~ ( SV14 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(196,plain,
! [SV15: $i] :
( ( ! [SY244: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SY244 @ SV15 ) @ SY244 )
| ~ ~ ( in @ ( sK15_Xx @ SY244 @ SV15 ) @ SV15 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY244 )
| ~ ( ~ ! [SY246: $i] :
( ~ ( in @ SY246 @ ( sK11_B @ SV15 ) )
| ! [SY247: $i] :
( ~ ( in @ SY247 @ SY246 )
| ( in @ SY247 @ ( sK13_SY205 @ SY244 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SY244 @ SV15 ) @ SY246 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SY244 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SY244 @ SV15 ) @ SY244 ) )
| ~ ! [SY248: $i] :
( ~ ( in @ SY248 @ ( sK13_SY205 @ SY244 @ SV15 ) )
| ~ ( in @ SY248 @ SY244 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(197,plain,
! [SV15: $i] :
( ( ~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SY250 @ ( sK11_B @ SV15 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(198,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
| ~ ~ ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
| ( SV16 = SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(199,plain,
! [SV17: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ~ ( in @ SY259 @ ( setadjoin @ SV17 @ SY258 ) )
| ( SY259 = SV17 )
| ( in @ SY259 @ SY258 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(200,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY260: $i,SY261: $i] :
( ( SY261 != SV17 )
| ( in @ SY261 @ ( setadjoin @ SV17 @ SY260 ) ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( in @ SY263 @ SY262 )
| ( in @ SY263 @ ( setadjoin @ SV17 @ SY262 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(201,plain,
! [SV18: $i > $i > $o,SV27: $i] :
( ( ( ~ ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
| ~ ! [SY284: $i] :
( ~ ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) )
| ~ ( ( SY284
!= ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) ) ) )
| ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SY284 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(202,plain,
! [SV19: $i,SV28: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) )
| ~ ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) ) )
= $false )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(203,plain,
! [SV20: $i] :
( ( ! [SY270: $i > $o,SY271: $i] :
( ~ ( in @ SY271 @ SV20 )
| ~ ( SY270 @ SY271 )
| ( in @ SY271
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY270 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(204,plain,
! [SV20: $i] :
( ( ! [SY273: $i > $o,SY274: $i] :
( ~ ( in @ SY274 @ SV20 )
| ~ ( in @ SY274
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY273 @ SX3 ) ) )
| ( SY273 @ SY274 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(205,plain,
! [SV21: $i,SV38: $i] :
( ( ( in @ SV38 @ SV21 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK10_B @ SV21 ) @ SV21 )
| ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ ( sK10_B @ SV21 ) )
| ~ ( in @ SY277 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(206,plain,
( ( sK1_SY0 = emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(207,plain,
! [SV44: $i] :
( ( ~ ( in @ SV44 @ sK1_SY0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(208,plain,
! [SV23: $i > $o,SV6: $i,SV32: $i] :
( ( ( in @ SV32
@ ( dsetconstr @ SV6
@ ^ [SY279: $i] : ( SV23 @ SY279 ) ) )
= $false )
| ( ( SV23 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(209,plain,
! [SV24: $i > $o,SV7: $i,SV33: $i] :
( ( ( in @ SV33
@ ( dsetconstr @ SV7
@ ^ [SY281: $i] : ( SV24 @ SY281 ) ) )
= $false )
| ( ( in @ SV33 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(210,plain,
! [SV25: $i > $o,SV8: $i,SV34: $i] :
( ( ( in @ SV34 @ SV8 )
= $false )
| ( ( ~ ( SV25 @ SV34 )
| ( in @ SV34
@ ( dsetconstr @ SV8
@ ^ [SY283: $i] : ( SV25 @ SY283 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(211,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV11 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV11 ) @ SV11 ) ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(212,plain,
! [SV11: $i] :
( ( ( ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(213,plain,
! [SV40: $i,SV45: $i] :
( ( ~ ( ~ ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV45 )
| ~ ~ ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV40 ) )
| ( in @ SV45 @ ( powerset @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(214,plain,
! [SV41: $i,SV46: $i] :
( ( ~ ( in @ SV46 @ ( powerset @ SV41 ) )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV46 )
| ( in @ SY300 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(215,plain,
! [SV42: $i,SV47: $i] :
( ( ! [SY301: $i] :
( ~ ( in @ SV47 @ SY301 )
| ~ ( in @ SY301 @ SV42 ) )
| ( in @ SV47 @ ( setunion @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(216,plain,
! [SV43: $i,SV48: $i] :
( ( ~ ( in @ SV48 @ ( setunion @ SV43 ) )
| ~ ( ~ ( in @ SV48 @ ( sK4_B @ SV48 @ SV43 ) )
| ~ ( in @ ( sK4_B @ SV48 @ SV43 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(217,plain,
! [SV35: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK20_SY84 @ SV35 @ SV12 ) )
| ~ ( ( SV35
!= ( sK20_SY84 @ SV35 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( SV12 @ SV35 ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(218,plain,
! [SV36: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK16_SY54 @ SV36 @ SV13 ) )
| ~ ( ( SV36
!= ( sK16_SY54 @ SV36 @ SV13 ) ) ) )
= $false )
| ( ( ~ ( SV13 @ SV36 ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(219,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
| ~ ( ( SV37
!= ( sK18_SY71 @ SV37 @ SV14 ) ) ) )
= $false )
| ( ( ~ ( SV14 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(220,plain,
! [SV15: $i,SV49: $i] :
( ( ~ ( ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
| ~ ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 ) )
| ! [SY302: $i] :
~ ( in @ SY302 @ SV49 )
| ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(221,plain,
! [SV15: $i] :
( ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SY250 @ ( sK11_B @ SV15 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(222,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
| ( SV16 = SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(223,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ~ ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
| ( SV16 = SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(224,plain,
! [SV50: $i,SV17: $i] :
( ( ! [SY306: $i] :
( ~ ( in @ SY306 @ ( setadjoin @ SV17 @ SV50 ) )
| ( SY306 = SV17 )
| ( in @ SY306 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(225,plain,
! [SV17: $i] :
( ( ~ ! [SY260: $i,SY261: $i] :
( ( SY261 != SV17 )
| ( in @ SY261 @ ( setadjoin @ SV17 @ SY260 ) ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( in @ SY263 @ SY262 )
| ( in @ SY263 @ ( setadjoin @ SV17 @ SY262 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(226,plain,
! [SV18: $i > $i > $o,SV27: $i] :
( ( ( ~ ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 ) )
= $false )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(227,plain,
! [SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ! [SY284: $i] :
( ~ ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) )
| ~ ( ( SY284
!= ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) ) ) )
| ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SY284 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(228,plain,
! [SV19: $i,SV28: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) ) )
= $false )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(229,plain,
! [SV19: $i,SV28: $i] :
( ( ( ~ ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) ) )
= $false )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(230,plain,
! [SV51: $i > $o,SV20: $i] :
( ( ! [SY307: $i] :
( ~ ( in @ SY307 @ SV20 )
| ~ ( SV51 @ SY307 )
| ( in @ SY307
@ ( dsetconstr @ SV20
@ ^ [SY308: $i] : ( SV51 @ SY308 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(231,plain,
! [SV52: $i > $o,SV20: $i] :
( ( ! [SY309: $i] :
( ~ ( in @ SY309 @ SV20 )
| ~ ( in @ SY309
@ ( dsetconstr @ SV20
@ ^ [SY310: $i] : ( SV52 @ SY310 ) ) )
| ( SV52 @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(232,plain,
! [SV38: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK10_B @ SV21 ) @ SV21 )
| ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ ( sK10_B @ SV21 ) )
| ~ ( in @ SY277 @ SV21 ) ) )
= $false )
| ( ( in @ SV38 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(233,plain,
! [SV44: $i] :
( ( in @ SV44 @ sK1_SY0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(234,plain,
! [SV8: $i,SV34: $i,SV25: $i > $o] :
( ( ( ~ ( SV25 @ SV34 ) )
= $true )
| ( ( in @ SV34
@ ( dsetconstr @ SV8
@ ^ [SY283: $i] : ( SV25 @ SY283 ) ) )
= $true )
| ( ( in @ SV34 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(235,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_Xx @ SV11 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(236,plain,
! [SV11: $i] :
( ( ( ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(237,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV45 )
| ~ ~ ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( in @ SV45 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(238,plain,
! [SV41: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( ! [SY300: $i] :
( ~ ( in @ SY300 @ SV46 )
| ( in @ SY300 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(239,plain,
! [SV42: $i,SV47: $i] :
( ( ( ! [SY301: $i] :
( ~ ( in @ SV47 @ SY301 )
| ~ ( in @ SY301 @ SV42 ) ) )
= $true )
| ( ( in @ SV47 @ ( setunion @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(240,plain,
! [SV43: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( setunion @ SV43 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV48 @ ( sK4_B @ SV48 @ SV43 ) )
| ~ ( in @ ( sK4_B @ SV48 @ SV43 ) @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(241,plain,
! [SV35: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK20_SY84 @ SV35 @ SV12 ) ) )
= $false )
| ( ( ~ ( SV12 @ SV35 ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(242,plain,
! [SV12: $i > $o,SV35: $i] :
( ( ( ~ ( ( SV35
!= ( sK20_SY84 @ SV35 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( SV12 @ SV35 ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(243,plain,
! [SV36: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK16_SY54 @ SV36 @ SV13 ) ) )
= $false )
| ( ( ~ ( SV13 @ SV36 ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(244,plain,
! [SV13: $i > $o,SV36: $i] :
( ( ( ~ ( ( SV36
!= ( sK16_SY54 @ SV36 @ SV13 ) ) ) )
= $false )
| ( ( ~ ( SV13 @ SV36 ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(245,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) ) )
= $false )
| ( ( ~ ( SV14 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(246,plain,
! [SV14: $i > $o,SV37: $i] :
( ( ( ~ ( ( SV37
!= ( sK18_SY71 @ SV37 @ SV14 ) ) ) )
= $false )
| ( ( ~ ( SV14 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(247,plain,
! [SV15: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
| ~ ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 ) )
| ! [SY302: $i] :
~ ( in @ SY302 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(248,plain,
! [SV15: $i] :
( ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SY250 @ ( sK11_B @ SV15 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(249,plain,
! [SV15: $i] :
( ( ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(250,plain,
! [SV16: $i,SV26: $i] :
( ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
| ( SV16 = SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(251,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
| ( SV16 = SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(252,plain,
! [SV50: $i,SV17: $i,SV53: $i] :
( ( ~ ( in @ SV53 @ ( setadjoin @ SV17 @ SV50 ) )
| ( SV53 = SV17 )
| ( in @ SV53 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(253,plain,
! [SV17: $i] :
( ( ~ ! [SY260: $i,SY261: $i] :
( ( SY261 != SV17 )
| ( in @ SY261 @ ( setadjoin @ SV17 @ SY260 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(254,plain,
! [SV17: $i] :
( ( ~ ! [SY262: $i,SY263: $i] :
( ~ ( in @ SY263 @ SY262 )
| ( in @ SY263 @ ( setadjoin @ SV17 @ SY262 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(255,plain,
! [SV18: $i > $i > $o,SV27: $i] :
( ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(256,plain,
! [SV27: $i,SV18: $i > $i > $o] :
( ( ( ! [SY284: $i] :
( ~ ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) )
| ~ ( ( SY284
!= ( sK9_SY200 @ SY284 @ SV27 @ SV18 ) ) ) )
| ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SY284 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(257,plain,
! [SV19: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) )
= $true )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(258,plain,
! [SV19: $i,SV28: $i] :
( ( ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
| ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) )
= $true )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(259,plain,
! [SV51: $i > $o,SV20: $i,SV54: $i] :
( ( ~ ( in @ SV54 @ SV20 )
| ~ ( SV51 @ SV54 )
| ( in @ SV54
@ ( dsetconstr @ SV20
@ ^ [SY308: $i] : ( SV51 @ SY308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(260,plain,
! [SV52: $i > $o,SV20: $i,SV55: $i] :
( ( ~ ( in @ SV55 @ SV20 )
| ~ ( in @ SV55
@ ( dsetconstr @ SV20
@ ^ [SY310: $i] : ( SV52 @ SY310 ) ) )
| ( SV52 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(261,plain,
! [SV38: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK10_B @ SV21 ) @ SV21 ) )
= $false )
| ( ( in @ SV38 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(262,plain,
! [SV38: $i,SV21: $i] :
( ( ( ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ ( sK10_B @ SV21 ) )
| ~ ( in @ SY277 @ SV21 ) ) )
= $false )
| ( ( in @ SV38 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(263,plain,
! [SV8: $i,SV34: $i,SV25: $i > $o] :
( ( ( SV25 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV8
@ ^ [SY283: $i] : ( SV25 @ SY283 ) ) )
= $true )
| ( ( in @ SV34 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(264,plain,
! [SV11: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV11 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV11 ) @ SV11 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(265,plain,
! [SV11: $i] :
( ( ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 )
= $false )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(266,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV45 )
| ~ ~ ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV40 ) )
= $false )
| ( ( in @ SV45 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(267,plain,
! [SV41: $i,SV46: $i] :
( ( ( in @ SV46 @ ( powerset @ SV41 ) )
= $false )
| ( ( ! [SY300: $i] :
( ~ ( in @ SY300 @ SV46 )
| ( in @ SY300 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(268,plain,
! [SV42: $i,SV56: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV56 )
| ~ ( in @ SV56 @ SV42 ) )
= $true )
| ( ( in @ SV47 @ ( setunion @ SV42 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(269,plain,
! [SV43: $i,SV48: $i] :
( ( ( in @ SV48 @ ( setunion @ SV43 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV48 @ ( sK4_B @ SV48 @ SV43 ) )
| ~ ( in @ ( sK4_B @ SV48 @ SV43 ) @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(270,plain,
! [SV35: $i,SV12: $i > $o] :
( ( ( SV12 @ ( sK20_SY84 @ SV35 @ SV12 ) )
= $true )
| ( ( ~ ( SV12 @ SV35 ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(271,plain,
! [SV12: $i > $o,SV35: $i] :
( ( ( SV35
!= ( sK20_SY84 @ SV35 @ SV12 ) )
= $true )
| ( ( ~ ( SV12 @ SV35 ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(272,plain,
! [SV36: $i,SV13: $i > $o] :
( ( ( SV13 @ ( sK16_SY54 @ SV36 @ SV13 ) )
= $true )
| ( ( ~ ( SV13 @ SV36 ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(273,plain,
! [SV13: $i > $o,SV36: $i] :
( ( ( SV36
!= ( sK16_SY54 @ SV36 @ SV13 ) )
= $true )
| ( ( ~ ( SV13 @ SV36 ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(274,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( ~ ( SV14 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(275,plain,
! [SV14: $i > $o,SV37: $i] :
( ( ( SV37
!= ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( ~ ( SV14 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(276,plain,
! [SV15: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
| ~ ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( ! [SY302: $i] :
~ ( in @ SY302 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(277,plain,
! [SV15: $i] :
( ( ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SY250 @ ( sK11_B @ SV15 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(278,plain,
! [SV15: $i] :
( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(279,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(280,plain,
! [SV16: $i,SV26: $i] :
( ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
| ( SV16 = SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(281,plain,
! [SV50: $i,SV17: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ ( setadjoin @ SV17 @ SV50 ) ) )
= $true )
| ( ( ( SV53 = SV17 )
| ( in @ SV53 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(282,plain,
! [SV17: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ( SY261 != SV17 )
| ( in @ SY261 @ ( setadjoin @ SV17 @ SY260 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(283,plain,
! [SV17: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ~ ( in @ SY263 @ SY262 )
| ( in @ SY263 @ ( setadjoin @ SV17 @ SY262 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(284,plain,
! [SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(285,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
| ~ ( ( SV57
!= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) ) ) )
| ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(286,plain,
! [SV19: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 ) )
= $true )
| ( ( ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) )
= $true )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(287,plain,
! [SV19: $i,SV28: $i] :
( ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
= $true )
| ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 )
= $true )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(288,plain,
! [SV51: $i > $o,SV20: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV20 ) )
= $true )
| ( ( ~ ( SV51 @ SV54 )
| ( in @ SV54
@ ( dsetconstr @ SV20
@ ^ [SY308: $i] : ( SV51 @ SY308 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(289,plain,
! [SV52: $i > $o,SV20: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV20 ) )
= $true )
| ( ( ~ ( in @ SV55
@ ( dsetconstr @ SV20
@ ^ [SY310: $i] : ( SV52 @ SY310 ) ) )
| ( SV52 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(290,plain,
! [SV38: $i,SV21: $i] :
( ( ( in @ ( sK10_B @ SV21 ) @ SV21 )
= $true )
| ( ( in @ SV38 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(291,plain,
! [SV38: $i,SV21: $i] :
( ( ( ! [SY277: $i] :
( ~ ( in @ SY277 @ ( sK10_B @ SV21 ) )
| ~ ( in @ SY277 @ SV21 ) ) )
= $true )
| ( ( in @ SV38 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(292,plain,
! [SV11: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV11 ) @ omega ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(293,plain,
! [SV11: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV11 ) @ SV11 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(294,plain,
! [SV11: $i] :
( ( ( in @ emptyset @ SV11 )
= $false )
| ( ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 )
= $false )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(295,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV45 ) )
= $false )
| ( ( in @ SV45 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(296,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ~ ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV40 ) )
= $false )
| ( ( in @ SV45 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(297,plain,
! [SV41: $i,SV46: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ SV46 )
| ( in @ SV58 @ SV41 ) )
= $true )
| ( ( in @ SV46 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(298,plain,
! [SV42: $i,SV56: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV56 ) )
= $true )
| ( ( ~ ( in @ SV56 @ SV42 ) )
= $true )
| ( ( in @ SV47 @ ( setunion @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(299,plain,
! [SV43: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( sK4_B @ SV48 @ SV43 ) )
| ~ ( in @ ( sK4_B @ SV48 @ SV43 ) @ SV43 ) )
= $false )
| ( ( in @ SV48 @ ( setunion @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(300,plain,
! [SV35: $i,SV12: $i > $o] :
( ( ( SV12 @ SV35 )
= $false )
| ( ( SV12 @ ( sK20_SY84 @ SV35 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(301,plain,
! [SV12: $i > $o,SV35: $i] :
( ( ( SV35
= ( sK20_SY84 @ SV35 @ SV12 ) )
= $false )
| ( ( ~ ( SV12 @ SV35 ) )
= $true )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(302,plain,
! [SV36: $i,SV13: $i > $o] :
( ( ( SV13 @ SV36 )
= $false )
| ( ( SV13 @ ( sK16_SY54 @ SV36 @ SV13 ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(303,plain,
! [SV13: $i > $o,SV36: $i] :
( ( ( SV36
= ( sK16_SY54 @ SV36 @ SV13 ) )
= $false )
| ( ( ~ ( SV13 @ SV36 ) )
= $true )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(304,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( SV14 @ SV37 )
= $false )
| ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(305,plain,
! [SV14: $i > $o,SV37: $i] :
( ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( ~ ( SV14 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(306,plain,
! [SV15: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
| ~ ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ! [SY302: $i] :
~ ( in @ SY302 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(307,plain,
! [SV15: $i,SV59: $i] :
( ( ! [SY313: $i] :
( ~ ( in @ SV59 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SY313 @ ( sK11_B @ SV15 ) )
| ! [SY314: $i] :
( ~ ( in @ SY314 @ SV59 )
| ( in @ SY314 @ SY313 ) )
| ! [SY315: $i] :
( ~ ( in @ SY315 @ SY313 )
| ( in @ SY315 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(308,plain,
! [SV15: $i] :
( ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(309,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
= $false )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(310,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(311,plain,
! [SV50: $i,SV17: $i,SV53: $i] :
( ( ( in @ SV53 @ ( setadjoin @ SV17 @ SV50 ) )
= $false )
| ( ( ( SV53 = SV17 )
| ( in @ SV53 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(312,plain,
! [SV60: $i,SV17: $i] :
( ( ! [SY316: $i] :
( ( SY316 != SV17 )
| ( in @ SY316 @ ( setadjoin @ SV17 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(313,plain,
! [SV17: $i,SV61: $i] :
( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ SV61 )
| ( in @ SY317 @ ( setadjoin @ SV17 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(314,plain,
! [SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(315,plain,
! [SV18: $i > $i > $o,SV27: $i] :
( ( ( ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(316,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
| ~ ( ( SV57
!= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) ) ) ) )
= $true )
| ( ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(317,plain,
! [SV19: $i,SV28: $i] :
( ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
= $false )
| ( ( ~ ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 ) )
= $true )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(318,plain,
! [SV51: $i > $o,SV20: $i,SV54: $i] :
( ( ( in @ SV54 @ SV20 )
= $false )
| ( ( ~ ( SV51 @ SV54 )
| ( in @ SV54
@ ( dsetconstr @ SV20
@ ^ [SY308: $i] : ( SV51 @ SY308 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(319,plain,
! [SV52: $i > $o,SV20: $i,SV55: $i] :
( ( ( in @ SV55 @ SV20 )
= $false )
| ( ( ~ ( in @ SV55
@ ( dsetconstr @ SV20
@ ^ [SY310: $i] : ( SV52 @ SY310 ) ) )
| ( SV52 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(320,plain,
! [SV38: $i,SV21: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK10_B @ SV21 ) )
| ~ ( in @ SV62 @ SV21 ) )
= $true )
| ( ( in @ SV38 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(321,plain,
! [SV11: $i] :
( ( ( in @ ( sK5_Xx @ SV11 ) @ omega )
= $true )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(322,plain,
! [SV11: $i] :
( ( ( in @ ( sK5_Xx @ SV11 ) @ SV11 )
= $true )
| ( ( ~ ( in @ emptyset @ SV11 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(323,plain,
! [SV11: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ omega )
| ( in @ SV63 @ SV11 ) )
= $true )
| ( ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 )
= $false )
| ( ( in @ emptyset @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(324,plain,
! [SV40: $i,SV45: $i] :
( ( ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV45 )
= $true )
| ( ( in @ SV45 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(325,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV40 ) )
= $true )
| ( ( in @ SV45 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(326,plain,
! [SV41: $i,SV46: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ SV46 ) )
= $true )
| ( ( in @ SV58 @ SV41 )
= $true )
| ( ( in @ SV46 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(327,plain,
! [SV42: $i,SV56: $i,SV47: $i] :
( ( ( in @ SV47 @ SV56 )
= $false )
| ( ( ~ ( in @ SV56 @ SV42 ) )
= $true )
| ( ( in @ SV47 @ ( setunion @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(328,plain,
! [SV43: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( sK4_B @ SV48 @ SV43 ) ) )
= $false )
| ( ( in @ SV48 @ ( setunion @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(329,plain,
! [SV43: $i,SV48: $i] :
( ( ( ~ ( in @ ( sK4_B @ SV48 @ SV43 ) @ SV43 ) )
= $false )
| ( ( in @ SV48 @ ( setunion @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(330,plain,
! [SV35: $i,SV12: $i > $o] :
( ( ( SV12 @ SV35 )
= $false )
| ( ( SV35
= ( sK20_SY84 @ SV35 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK19_Xx @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(331,plain,
! [SV36: $i,SV13: $i > $o] :
( ( ( SV13 @ SV36 )
= $false )
| ( ( SV36
= ( sK16_SY54 @ SV36 @ SV13 ) )
= $false )
| ( ( SV13
@ ( descr
@ ^ [SY241: $i] : ( SV13 @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(332,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) )
= $false )
| ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(333,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( SV14 @ SV37 )
= $false )
| ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(334,plain,
! [SV15: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 ) )
= $false )
| ( ( ! [SY302: $i] :
~ ( in @ SY302 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(335,plain,
! [SV15: $i,SV49: $i] :
( ( ( ~ ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ! [SY302: $i] :
~ ( in @ SY302 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(336,plain,
! [SV64: $i,SV15: $i,SV59: $i] :
( ( ~ ( in @ SV59 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SV64 @ ( sK11_B @ SV15 ) )
| ! [SY318: $i] :
( ~ ( in @ SY318 @ SV59 )
| ( in @ SY318 @ SV64 ) )
| ! [SY319: $i] :
( ~ ( in @ SY319 @ SV64 )
| ( in @ SY319 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(337,plain,
! [SV15: $i] :
( ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(338,plain,
! [SV15: $i] :
( ( ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(339,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 ) )
= $false )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(340,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
= $false )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(341,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
| ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
= $false )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(342,plain,
! [SV50: $i,SV17: $i,SV53: $i] :
( ( ( SV53 = SV17 )
= $true )
| ( ( in @ SV53 @ SV50 )
= $true )
| ( ( in @ SV53 @ ( setadjoin @ SV17 @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(343,plain,
! [SV60: $i,SV17: $i,SV65: $i] :
( ( ( SV65 != SV17 )
| ( in @ SV65 @ ( setadjoin @ SV17 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(344,plain,
! [SV17: $i,SV61: $i,SV66: $i] :
( ( ~ ( in @ SV66 @ SV61 )
| ( in @ SV66 @ ( setadjoin @ SV17 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(345,plain,
! [SV27: $i,SV18: $i > $i > $o] :
( ( ( ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(346,plain,
! [SV18: $i > $i > $o,SV27: $i] :
( ( ( ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(347,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
| ~ ( ( SV57
!= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) ) ) )
= $false )
| ( ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(348,plain,
! [SV19: $i,SV28: $i] :
( ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV28 )
= $false )
| ( ( in @ ( sK2_Xx @ SV28 @ SV19 ) @ SV19 )
= $false )
| ( ( SV19 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(349,plain,
! [SV20: $i,SV54: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV54 ) )
= $true )
| ( ( in @ SV54
@ ( dsetconstr @ SV20
@ ^ [SY308: $i] : ( SV51 @ SY308 ) ) )
= $true )
| ( ( in @ SV54 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(350,plain,
! [SV52: $i > $o,SV20: $i,SV55: $i] :
( ( ( ~ ( in @ SV55
@ ( dsetconstr @ SV20
@ ^ [SY310: $i] : ( SV52 @ SY310 ) ) ) )
= $true )
| ( ( SV52 @ SV55 )
= $true )
| ( ( in @ SV55 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(351,plain,
! [SV38: $i,SV21: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK10_B @ SV21 ) ) )
= $true )
| ( ( ~ ( in @ SV62 @ SV21 ) )
= $true )
| ( ( in @ SV38 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(352,plain,
! [SV11: $i] :
( ( ( in @ emptyset @ SV11 )
= $false )
| ( ( in @ ( sK5_Xx @ SV11 ) @ omega )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(353,plain,
! [SV11: $i] :
( ( ( in @ emptyset @ SV11 )
= $false )
| ( ( in @ ( sK5_Xx @ SV11 ) @ SV11 )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( in @ SY238 @ omega )
| ( in @ SY238 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(354,plain,
! [SV11: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ omega ) )
= $true )
| ( ( in @ SV63 @ SV11 )
= $true )
| ( ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 )
= $false )
| ( ( in @ emptyset @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(355,plain,
! [SV40: $i,SV45: $i] :
( ( ( in @ ( sK3_Xx @ SV45 @ SV40 ) @ SV40 )
= $false )
| ( ( in @ SV45 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(356,plain,
! [SV41: $i,SV46: $i,SV58: $i] :
( ( ( in @ SV58 @ SV46 )
= $false )
| ( ( in @ SV58 @ SV41 )
= $true )
| ( ( in @ SV46 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(357,plain,
! [SV47: $i,SV42: $i,SV56: $i] :
( ( ( in @ SV56 @ SV42 )
= $false )
| ( ( in @ SV47 @ SV56 )
= $false )
| ( ( in @ SV47 @ ( setunion @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(358,plain,
! [SV43: $i,SV48: $i] :
( ( ( in @ SV48 @ ( sK4_B @ SV48 @ SV43 ) )
= $true )
| ( ( in @ SV48 @ ( setunion @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(359,plain,
! [SV43: $i,SV48: $i] :
( ( ( in @ ( sK4_B @ SV48 @ SV43 ) @ SV43 )
= $true )
| ( ( in @ SV48 @ ( setunion @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(360,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) ) )
= $false )
| ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(361,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) )
= $false )
| ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(362,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) )
| ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) )
= $false )
| ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(363,plain,
! [SV15: $i,SV49: $i] :
( ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( ! [SY302: $i] :
~ ( in @ SY302 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(364,plain,
! [SV15: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 ) )
= $true )
| ( ( ! [SY302: $i] :
~ ( in @ SY302 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(365,plain,
! [SV64: $i,SV15: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ ( sK11_B @ SV15 ) )
| ~ ( in @ SV64 @ ( sK11_B @ SV15 ) ) )
= $true )
| ( ( ! [SY318: $i] :
( ~ ( in @ SY318 @ SV59 )
| ( in @ SY318 @ SV64 ) )
| ! [SY319: $i] :
( ~ ( in @ SY319 @ SV64 )
| ( in @ SY319 @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(366,plain,
! [SV15: $i] :
( ( ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK11_B @ SV15 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(367,plain,
! [SV15: $i] :
( ( ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV15 )
| ~ ( in @ SY256 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ~ ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) )
| ~ ( ( in @ SY255 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) )
| ( in @ SY256 @ ( sK12_SY218 @ SY256 @ SY255 @ SV15 ) ) ) ) )
| ( SY255 = SY256 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(368,plain,
! [SV16: $i,SV26: $i] :
( ( ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
= $true )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(369,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
= $true )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(370,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 ) )
= $false )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(371,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
= $false )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(372,plain,
! [SV60: $i,SV17: $i,SV65: $i] :
( ( ( SV65 != SV17 )
= $true )
| ( ( in @ SV65 @ ( setadjoin @ SV17 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(373,plain,
! [SV17: $i,SV61: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ SV61 ) )
= $true )
| ( ( in @ SV66 @ ( setadjoin @ SV17 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(374,plain,
! [SV27: $i,SV67: $i,SV18: $i > $i > $o] :
( ( ( ! [SY320: $i] :
( ~ ( SV18 @ SY320 @ SV67 )
| ~ ( in @ SY320 @ SV27 ) )
| ( in @ SV67 @ ( sK6_B @ SV27 @ SV18 ) ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(375,plain,
! [SV18: $i > $i > $o,SV27: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV68 )
| ~ ( in @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV27 ) ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(376,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) ) )
= $false )
| ( ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(377,plain,
! [SV18: $i > $i > $o,SV27: $i,SV57: $i] :
( ( ( ~ ( ( SV57
!= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) ) ) )
= $false )
| ( ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(378,plain,
! [SV20: $i,SV54: $i,SV51: $i > $o] :
( ( ( SV51 @ SV54 )
= $false )
| ( ( in @ SV54
@ ( dsetconstr @ SV20
@ ^ [SY308: $i] : ( SV51 @ SY308 ) ) )
= $true )
| ( ( in @ SV54 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(379,plain,
! [SV52: $i > $o,SV20: $i,SV55: $i] :
( ( ( in @ SV55
@ ( dsetconstr @ SV20
@ ^ [SY310: $i] : ( SV52 @ SY310 ) ) )
= $false )
| ( ( SV52 @ SV55 )
= $true )
| ( ( in @ SV55 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(380,plain,
! [SV38: $i,SV21: $i,SV62: $i] :
( ( ( in @ SV62 @ ( sK10_B @ SV21 ) )
= $false )
| ( ( ~ ( in @ SV62 @ SV21 ) )
= $true )
| ( ( in @ SV38 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(381,plain,
! [SV11: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ omega )
| ( in @ SV69 @ SV11 ) )
= $true )
| ( ( in @ ( sK5_Xx @ SV11 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(382,plain,
! [SV11: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ omega )
| ( in @ SV70 @ SV11 ) )
= $true )
| ( ( in @ ( sK5_Xx @ SV11 ) @ SV11 )
= $true )
| ( ( in @ emptyset @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(383,plain,
! [SV11: $i,SV63: $i] :
( ( ( in @ SV63 @ omega )
= $false )
| ( ( in @ SV63 @ SV11 )
= $true )
| ( ( in @ ( setadjoin @ ( sK5_Xx @ SV11 ) @ ( sK5_Xx @ SV11 ) ) @ SV11 )
= $false )
| ( ( in @ emptyset @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(384,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) ) )
= $true )
| ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(385,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( SV14 @ ( sK17_Xx @ SV14 ) )
= $true )
| ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(386,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) ) )
= $false )
| ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(387,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK17_Xx @ SV14 ) ) )
= $false )
| ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(388,plain,
! [SV15: $i,SV49: $i,SV71: $i] :
( ( ( ~ ( in @ SV71 @ SV49 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(389,plain,
! [SV15: $i,SV49: $i] :
( ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( ! [SY302: $i] :
~ ( in @ SY302 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(390,plain,
! [SV64: $i,SV15: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ ( sK11_B @ SV15 ) ) )
= $true )
| ( ( ~ ( in @ SV64 @ ( sK11_B @ SV15 ) ) )
= $true )
| ( ( ! [SY318: $i] :
( ~ ( in @ SY318 @ SV59 )
| ( in @ SY318 @ SV64 ) )
| ! [SY319: $i] :
( ~ ( in @ SY319 @ SV64 )
| ( in @ SY319 @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(391,plain,
! [SV15: $i,SV72: $i] :
( ( ~ ( in @ SV72 @ ( sK11_B @ SV15 ) )
| ! [SY321: $i] :
( ~ ( in @ SY321 @ SV72 )
| ( in @ SY321 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(392,plain,
! [SV15: $i,SV73: $i] :
( ( ! [SY322: $i] :
( ~ ( in @ SV73 @ SV15 )
| ~ ( in @ SY322 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SY322 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SY322 @ SV73 @ SV15 ) )
| ~ ( in @ SY322 @ ( sK12_SY218 @ SY322 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SY322 @ SV73 @ SV15 ) )
| ( in @ SY322 @ ( sK12_SY218 @ SY322 @ SV73 @ SV15 ) ) ) ) )
| ( SV73 = SY322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(393,plain,
! [SV16: $i,SV26: $i] :
( ( ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 )
= $false )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(394,plain,
! [SV16: $i,SV26: $i] :
( ( ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV26 )
= $true )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(395,plain,
! [SV16: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 ) )
= $true )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(396,plain,
! [SV60: $i,SV17: $i,SV65: $i] :
( ( ( SV65 = SV17 )
= $false )
| ( ( in @ SV65 @ ( setadjoin @ SV17 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(397,plain,
! [SV17: $i,SV61: $i,SV66: $i] :
( ( ( in @ SV66 @ SV61 )
= $false )
| ( ( in @ SV66 @ ( setadjoin @ SV17 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(398,plain,
! [SV27: $i,SV67: $i,SV18: $i > $i > $o] :
( ( ( ! [SY320: $i] :
( ~ ( SV18 @ SY320 @ SV67 )
| ~ ( in @ SY320 @ SV27 ) ) )
= $true )
| ( ( in @ SV67 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(399,plain,
! [SV18: $i > $i > $o,SV27: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ ( sK6_B @ SV27 @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( SV18 @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV68 )
| ~ ( in @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV27 ) ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(400,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(401,plain,
! [SV18: $i > $i > $o,SV27: $i,SV57: $i] :
( ( ( SV57
!= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(402,plain,
! [SV38: $i,SV21: $i,SV62: $i] :
( ( ( in @ SV62 @ SV21 )
= $false )
| ( ( in @ SV62 @ ( sK10_B @ SV21 ) )
= $false )
| ( ( in @ SV38 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(403,plain,
! [SV11: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ omega ) )
= $true )
| ( ( in @ SV69 @ SV11 )
= $true )
| ( ( in @ ( sK5_Xx @ SV11 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(404,plain,
! [SV11: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ omega ) )
= $true )
| ( ( in @ SV70 @ SV11 )
= $true )
| ( ( in @ ( sK5_Xx @ SV11 ) @ SV11 )
= $true )
| ( ( in @ emptyset @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(405,plain,
! [SV37: $i,SV74: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ SV74 )
| ( ( sK17_Xx @ SV14 )
= SV74 ) )
= $true )
| ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(406,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( ! [SY243: $i] :
( ~ ( SV14 @ SY243 )
| ( ( sK17_Xx @ SV14 )
= SY243 ) ) )
= $true )
| ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(407,plain,
! [SV37: $i,SV14: $i > $o] :
( ( ( SV14 @ ( sK17_Xx @ SV14 ) )
= $true )
| ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(408,plain,
! [SV15: $i,SV49: $i,SV71: $i] :
( ( ( in @ SV71 @ SV49 )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(409,plain,
! [SV15: $i,SV49: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV49 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(410,plain,
! [SV64: $i,SV15: $i,SV59: $i] :
( ( ( in @ SV59 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( ~ ( in @ SV64 @ ( sK11_B @ SV15 ) ) )
= $true )
| ( ( ! [SY318: $i] :
( ~ ( in @ SY318 @ SV59 )
| ( in @ SY318 @ SV64 ) )
| ! [SY319: $i] :
( ~ ( in @ SY319 @ SV64 )
| ( in @ SY319 @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(411,plain,
! [SV15: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ ( sK11_B @ SV15 ) ) )
= $true )
| ( ( ! [SY321: $i] :
( ~ ( in @ SY321 @ SV72 )
| ( in @ SY321 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(412,plain,
! [SV76: $i,SV15: $i,SV73: $i] :
( ( ~ ( in @ SV73 @ SV15 )
| ~ ( in @ SV76 @ SV15 )
| ~ ( ~ ( in @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) ) )
| ( SV73 = SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(413,plain,
! [SV16: $i,SV26: $i] :
( ( ( in @ ( sK21_Xx @ SV26 @ SV16 ) @ SV16 )
= $false )
| ( ( SV16 = SV26 )
= $true )
| ( ( in @ ( sK22_Xx @ SV26 @ SV16 ) @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(414,plain,
! [SV27: $i,SV67: $i,SV77: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ SV77 @ SV67 )
| ~ ( in @ SV77 @ SV27 ) )
= $true )
| ( ( in @ SV67 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(415,plain,
! [SV18: $i > $i > $o,SV27: $i,SV68: $i] :
( ( ( in @ SV68 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( SV18 @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV68 )
| ~ ( in @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV27 ) ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(416,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(417,plain,
! [SV18: $i > $i > $o,SV27: $i,SV57: $i] :
( ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( ~ ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(418,plain,
! [SV11: $i,SV69: $i] :
( ( ( in @ SV69 @ omega )
= $false )
| ( ( in @ SV69 @ SV11 )
= $true )
| ( ( in @ ( sK5_Xx @ SV11 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(419,plain,
! [SV11: $i,SV70: $i] :
( ( ( in @ SV70 @ omega )
= $false )
| ( ( in @ SV70 @ SV11 )
= $true )
| ( ( in @ ( sK5_Xx @ SV11 ) @ SV11 )
= $true )
| ( ( in @ emptyset @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(420,plain,
! [SV37: $i,SV74: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ SV74 ) )
= $true )
| ( ( ( sK17_Xx @ SV14 )
= SV74 )
= $true )
| ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(421,plain,
! [SV37: $i,SV78: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ SV78 )
| ( ( sK17_Xx @ SV14 )
= SV78 ) )
= $true )
| ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(422,plain,
! [SV71: $i,SV49: $i,SV15: $i] :
( ( ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(423,plain,
! [SV15: $i,SV49: $i,SV75: $i] :
( ( ( in @ SV75 @ SV49 )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(424,plain,
! [SV59: $i,SV15: $i,SV64: $i] :
( ( ( in @ SV64 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ SV59 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( ! [SY318: $i] :
( ~ ( in @ SY318 @ SV59 )
| ( in @ SY318 @ SV64 ) )
| ! [SY319: $i] :
( ~ ( in @ SY319 @ SV64 )
| ( in @ SY319 @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(425,plain,
! [SV15: $i,SV72: $i] :
( ( ( in @ SV72 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( ! [SY321: $i] :
( ~ ( in @ SY321 @ SV72 )
| ( in @ SY321 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(426,plain,
! [SV76: $i,SV15: $i,SV73: $i] :
( ( ( ~ ( in @ SV73 @ SV15 )
| ~ ( in @ SV76 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) ) )
| ( SV73 = SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(427,plain,
! [SV27: $i,SV67: $i,SV77: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ SV77 @ SV67 ) )
= $true )
| ( ( ~ ( in @ SV77 @ SV27 ) )
= $true )
| ( ( in @ SV67 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(428,plain,
! [SV27: $i,SV68: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV68 )
| ~ ( in @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV27 ) )
= $false )
| ( ( in @ SV68 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(429,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(430,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( ~ ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(431,plain,
! [SV37: $i,SV74: $i,SV14: $i > $o] :
( ( ( SV14 @ SV74 )
= $false )
| ( ( ( sK17_Xx @ SV14 )
= SV74 )
= $true )
| ( ( SV14 @ ( sK18_SY71 @ SV37 @ SV14 ) )
= $true )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(432,plain,
! [SV37: $i,SV78: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ SV78 ) )
= $true )
| ( ( ( sK17_Xx @ SV14 )
= SV78 )
= $true )
| ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(433,plain,
! [SV71: $i,SV49: $i,SV15: $i] :
( ( ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(434,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(435,plain,
! [SV75: $i,SV49: $i,SV15: $i] :
( ( ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(436,plain,
! [SV15: $i,SV64: $i,SV59: $i] :
( ( ( ! [SY318: $i] :
( ~ ( in @ SY318 @ SV59 )
| ( in @ SY318 @ SV64 ) ) )
= $true )
| ( ( ! [SY319: $i] :
( ~ ( in @ SY319 @ SV64 )
| ( in @ SY319 @ SV59 ) ) )
= $true )
| ( ( in @ SV59 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ SV64 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(437,plain,
! [SV15: $i,SV72: $i,SV79: $i] :
( ( ( ~ ( in @ SV79 @ SV72 )
| ( in @ SV79 @ SV15 ) )
= $true )
| ( ( in @ SV72 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(438,plain,
! [SV76: $i,SV15: $i,SV73: $i] :
( ( ( ~ ( in @ SV73 @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV76 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) ) )
| ( SV73 = SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(439,plain,
! [SV27: $i,SV67: $i,SV77: $i,SV18: $i > $i > $o] :
( ( ( SV18 @ SV77 @ SV67 )
= $false )
| ( ( ~ ( in @ SV77 @ SV27 ) )
= $true )
| ( ( in @ SV67 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(440,plain,
! [SV27: $i,SV68: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV68 ) )
= $false )
| ( ( in @ SV68 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(441,plain,
! [SV18: $i > $i > $o,SV27: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV27 ) )
= $false )
| ( ( in @ SV68 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(442,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(443,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i] :
( ( ( ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(444,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) )
| ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) )
= $false )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(445,plain,
! [SV37: $i,SV78: $i,SV14: $i > $o] :
( ( ( SV14 @ SV78 )
= $false )
| ( ( ( sK17_Xx @ SV14 )
= SV78 )
= $true )
| ( ( SV37
= ( sK18_SY71 @ SV37 @ SV14 ) )
= $false )
| ( ( SV14 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(446,plain,
! [SV71: $i,SV49: $i,SV15: $i] :
( ( ( ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(447,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(448,plain,
! [SV75: $i,SV49: $i,SV15: $i] :
( ( ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(449,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(450,plain,
! [SV15: $i,SV64: $i,SV59: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV59 )
| ( in @ SV80 @ SV64 ) )
= $true )
| ( ( ! [SY319: $i] :
( ~ ( in @ SY319 @ SV64 )
| ( in @ SY319 @ SV59 ) ) )
= $true )
| ( ( in @ SV59 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ SV64 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(451,plain,
! [SV15: $i,SV72: $i,SV79: $i] :
( ( ( ~ ( in @ SV79 @ SV72 ) )
= $true )
| ( ( in @ SV79 @ SV15 )
= $true )
| ( ( in @ SV72 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(452,plain,
! [SV76: $i,SV15: $i,SV73: $i] :
( ( ( in @ SV73 @ SV15 )
= $false )
| ( ( ~ ( in @ SV76 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) ) )
| ( SV73 = SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(453,plain,
! [SV67: $i,SV18: $i > $i > $o,SV27: $i,SV77: $i] :
( ( ( in @ SV77 @ SV27 )
= $false )
| ( ( SV18 @ SV77 @ SV67 )
= $false )
| ( ( in @ SV67 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(454,plain,
! [SV27: $i,SV68: $i,SV18: $i > $i > $o] :
( ( ( SV18 @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV68 )
= $true )
| ( ( in @ SV68 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(455,plain,
! [SV18: $i > $i > $o,SV27: $i,SV68: $i] :
( ( ( in @ ( sK7_Xy @ SV68 @ SV27 @ SV18 ) @ SV27 )
= $true )
| ( ( in @ SV68 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(456,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(457,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i] :
( ( ( ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(458,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ~ ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) ) )
= $false )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(459,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i] :
( ( ( ~ ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) )
= $false )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(460,plain,
! [SV71: $i,SV49: $i,SV15: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ ( sK11_B @ SV15 ) )
| ! [SY323: $i] :
( ~ ( in @ SY323 @ SV81 )
| ( in @ SY323 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV81 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(461,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(462,plain,
! [SV75: $i,SV49: $i,SV15: $i] :
( ( ( ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK11_B @ SV15 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SY303 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(463,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(464,plain,
! [SV15: $i,SV64: $i,SV59: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV59 ) )
= $true )
| ( ( in @ SV80 @ SV64 )
= $true )
| ( ( ! [SY319: $i] :
( ~ ( in @ SY319 @ SV64 )
| ( in @ SY319 @ SV59 ) ) )
= $true )
| ( ( in @ SV59 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ SV64 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(465,plain,
! [SV15: $i,SV72: $i,SV79: $i] :
( ( ( in @ SV79 @ SV72 )
= $false )
| ( ( in @ SV79 @ SV15 )
= $true )
| ( ( in @ SV72 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(466,plain,
! [SV73: $i,SV15: $i,SV76: $i] :
( ( ( in @ SV76 @ SV15 )
= $false )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) ) )
| ( SV73 = SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(467,plain,
! [SV57: $i,SV27: $i,SV82: $i,SV18: $i > $i > $o] :
( ( ( ! [SY324: $i] :
( ~ ( SV18 @ SY324 @ SV82 )
| ~ ( in @ SY324 @ SV27 ) )
| ( in @ SV82 @ ( sK6_B @ SV27 @ SV18 ) ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(468,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV83 )
| ~ ( in @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV27 ) ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(469,plain,
! [SV57: $i,SV27: $i,SV18: $i > $i > $o] :
( ( ( ! [SY285: $i] :
( ! [SY286: $i] :
( ~ ( SV18 @ SY286 @ SY285 )
| ~ ( in @ SY286 @ SV27 ) )
| ( in @ SY285 @ ( sK6_B @ SV27 @ SV18 ) ) ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(470,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i] :
( ( ( ! [SY287: $i] :
( ~ ( in @ SY287 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SY287 )
| ~ ( in @ ( sK7_Xy @ SY287 @ SV27 @ SV18 ) @ SV27 ) ) ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(471,plain,
! [SV71: $i,SV49: $i,SV15: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ ( sK11_B @ SV15 ) ) )
= $true )
| ( ( ! [SY323: $i] :
( ~ ( in @ SY323 @ SV81 )
| ( in @ SY323 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV81 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(472,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(473,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(474,plain,
! [SV75: $i,SV49: $i,SV15: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ ( sK11_B @ SV15 ) )
| ! [SY325: $i] :
( ~ ( in @ SY325 @ SV84 )
| ( in @ SY325 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV84 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(475,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
| ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(476,plain,
! [SV15: $i,SV64: $i,SV59: $i,SV80: $i] :
( ( ( in @ SV80 @ SV59 )
= $false )
| ( ( in @ SV80 @ SV64 )
= $true )
| ( ( ! [SY319: $i] :
( ~ ( in @ SY319 @ SV64 )
| ( in @ SY319 @ SV59 ) ) )
= $true )
| ( ( in @ SV59 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ SV64 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(477,plain,
! [SV15: $i,SV73: $i,SV76: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) ) ) )
= $true )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(478,plain,
! [SV57: $i,SV27: $i,SV82: $i,SV18: $i > $i > $o] :
( ( ( ! [SY324: $i] :
( ~ ( SV18 @ SY324 @ SV82 )
| ~ ( in @ SY324 @ SV27 ) ) )
= $true )
| ( ( in @ SV82 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(479,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( sK6_B @ SV27 @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( SV18 @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV83 )
| ~ ( in @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV27 ) ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(480,plain,
! [SV57: $i,SV27: $i,SV85: $i,SV18: $i > $i > $o] :
( ( ( ! [SY326: $i] :
( ~ ( SV18 @ SY326 @ SV85 )
| ~ ( in @ SY326 @ SV27 ) )
| ( in @ SV85 @ ( sK6_B @ SV27 @ SV18 ) ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(481,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV86: $i] :
( ( ( ~ ( in @ SV86 @ ( sK6_B @ SV27 @ SV18 ) )
| ~ ( ~ ( SV18 @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV86 )
| ~ ( in @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV27 ) ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(482,plain,
! [SV71: $i,SV49: $i,SV15: $i,SV81: $i] :
( ( ( in @ SV81 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( ! [SY323: $i] :
( ~ ( in @ SY323 @ SV81 )
| ( in @ SY323 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV81 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(483,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(484,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(485,plain,
! [SV75: $i,SV49: $i,SV15: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ ( sK11_B @ SV15 ) ) )
= $true )
| ( ( ! [SY325: $i] :
( ~ ( in @ SY325 @ SV84 )
| ( in @ SY325 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV84 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(486,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(487,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(488,plain,
! [SV15: $i,SV80: $i,SV59: $i,SV64: $i,SV87: $i] :
( ( ( ~ ( in @ SV87 @ SV64 )
| ( in @ SV87 @ SV59 ) )
= $true )
| ( ( in @ SV80 @ SV64 )
= $true )
| ( ( in @ SV80 @ SV59 )
= $false )
| ( ( in @ SV59 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ SV64 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(489,plain,
! [SV15: $i,SV73: $i,SV76: $i] :
( ( ( ~ ( in @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) ) )
= $false )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(490,plain,
! [SV57: $i,SV27: $i,SV82: $i,SV88: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ SV88 @ SV82 )
| ~ ( in @ SV88 @ SV27 ) )
= $true )
| ( ( in @ SV82 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(491,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV83: $i] :
( ( ( in @ SV83 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( SV18 @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV83 )
| ~ ( in @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV27 ) ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(492,plain,
! [SV57: $i,SV27: $i,SV85: $i,SV18: $i > $i > $o] :
( ( ( ! [SY326: $i] :
( ~ ( SV18 @ SY326 @ SV85 )
| ~ ( in @ SY326 @ SV27 ) ) )
= $true )
| ( ( in @ SV85 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(493,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV86: $i] :
( ( ( ~ ( in @ SV86 @ ( sK6_B @ SV27 @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( SV18 @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV86 )
| ~ ( in @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV27 ) ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(494,plain,
! [SV71: $i,SV15: $i,SV49: $i,SV81: $i] :
( ( ( ! [SY323: $i] :
( ~ ( in @ SY323 @ SV81 )
| ( in @ SY323 @ ( sK13_SY205 @ SV49 @ SV15 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV81 )
= $true )
| ( ( in @ SV81 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(495,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(496,plain,
! [SV71: $i,SV15: $i,SV49: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SV89 @ SV49 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(497,plain,
! [SV75: $i,SV49: $i,SV15: $i,SV84: $i] :
( ( ( in @ SV84 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( ! [SY325: $i] :
( ~ ( in @ SY325 @ SV84 )
| ( in @ SY325 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
| ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV84 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(498,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(499,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ! [SY305: $i] :
( ~ ( in @ SY305 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SY305 @ SV49 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(500,plain,
! [SV15: $i,SV80: $i,SV59: $i,SV64: $i,SV87: $i] :
( ( ( ~ ( in @ SV87 @ SV64 ) )
= $true )
| ( ( in @ SV87 @ SV59 )
= $true )
| ( ( in @ SV80 @ SV64 )
= $true )
| ( ( in @ SV80 @ SV59 )
= $false )
| ( ( in @ SV59 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ SV64 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(501,plain,
! [SV15: $i,SV73: $i,SV76: $i] :
( ( ( ~ ( in @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) ) )
= $false )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(502,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) ) )
= $false )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(503,plain,
! [SV57: $i,SV27: $i,SV82: $i,SV88: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ SV88 @ SV82 ) )
= $true )
| ( ( ~ ( in @ SV88 @ SV27 ) )
= $true )
| ( ( in @ SV82 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(504,plain,
! [SV57: $i,SV27: $i,SV83: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV83 )
| ~ ( in @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV27 ) )
= $false )
| ( ( in @ SV83 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(505,plain,
! [SV57: $i,SV27: $i,SV85: $i,SV90: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ SV90 @ SV85 )
| ~ ( in @ SV90 @ SV27 ) )
= $true )
| ( ( in @ SV85 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(506,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV86: $i] :
( ( ( in @ SV86 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( SV18 @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV86 )
| ~ ( in @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV27 ) ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(507,plain,
! [SV71: $i,SV15: $i,SV49: $i,SV81: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ SV81 )
| ( in @ SV91 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
= $true )
| ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV81 )
= $true )
| ( ( in @ SV81 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(508,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(509,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(510,plain,
! [SV71: $i,SV15: $i,SV49: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
= $true )
| ( ( ~ ( in @ SV89 @ SV49 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(511,plain,
! [SV75: $i,SV15: $i,SV49: $i,SV84: $i] :
( ( ( ! [SY325: $i] :
( ~ ( in @ SY325 @ SV84 )
| ( in @ SY325 @ ( sK13_SY205 @ SV49 @ SV15 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV84 )
= $true )
| ( ( in @ SV84 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(512,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
| ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(513,plain,
! [SV75: $i,SV15: $i,SV49: $i,SV92: $i] :
( ( ( ~ ( in @ SV92 @ ( sK13_SY205 @ SV49 @ SV15 ) )
| ~ ( in @ SV92 @ SV49 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(514,plain,
! [SV15: $i,SV80: $i,SV59: $i,SV64: $i,SV87: $i] :
( ( ( in @ SV87 @ SV64 )
= $false )
| ( ( in @ SV87 @ SV59 )
= $true )
| ( ( in @ SV80 @ SV64 )
= $true )
| ( ( in @ SV80 @ SV59 )
= $false )
| ( ( in @ SV59 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ SV64 @ ( sK11_B @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(515,plain,
! [SV15: $i,SV73: $i,SV76: $i] :
( ( ( in @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) @ ( sK11_B @ SV15 ) )
= $true )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(516,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) ) )
= $true )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(517,plain,
! [SV57: $i,SV27: $i,SV82: $i,SV88: $i,SV18: $i > $i > $o] :
( ( ( SV18 @ SV88 @ SV82 )
= $false )
| ( ( ~ ( in @ SV88 @ SV27 ) )
= $true )
| ( ( in @ SV82 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(518,plain,
! [SV57: $i,SV27: $i,SV83: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV83 ) )
= $false )
| ( ( in @ SV83 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(519,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV83: $i] :
( ( ( ~ ( in @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV27 ) )
= $false )
| ( ( in @ SV83 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(520,plain,
! [SV57: $i,SV27: $i,SV85: $i,SV90: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ SV90 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV90 @ SV27 ) )
= $true )
| ( ( in @ SV85 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(521,plain,
! [SV57: $i,SV27: $i,SV86: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV86 )
| ~ ( in @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV27 ) )
= $false )
| ( ( in @ SV86 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(522,plain,
! [SV71: $i,SV15: $i,SV49: $i,SV81: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ SV81 ) )
= $true )
| ( ( in @ SV91 @ ( sK13_SY205 @ SV49 @ SV15 ) )
= $true )
| ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV81 )
= $true )
| ( ( in @ SV81 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(523,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(524,plain,
! [SV71: $i,SV15: $i,SV49: $i] :
( ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(525,plain,
! [SV71: $i,SV15: $i,SV49: $i,SV89: $i] :
( ( ( in @ SV89 @ ( sK13_SY205 @ SV49 @ SV15 ) )
= $false )
| ( ( ~ ( in @ SV89 @ SV49 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(526,plain,
! [SV75: $i,SV15: $i,SV49: $i,SV84: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ SV84 )
| ( in @ SV93 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
= $true )
| ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV84 )
= $true )
| ( ( in @ SV84 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(527,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(528,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(529,plain,
! [SV75: $i,SV15: $i,SV49: $i,SV92: $i] :
( ( ( ~ ( in @ SV92 @ ( sK13_SY205 @ SV49 @ SV15 ) ) )
= $true )
| ( ( ~ ( in @ SV92 @ SV49 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(530,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
| ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) )
= $false )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(531,plain,
! [SV57: $i,SV82: $i,SV18: $i > $i > $o,SV27: $i,SV88: $i] :
( ( ( in @ SV88 @ SV27 )
= $false )
| ( ( SV18 @ SV88 @ SV82 )
= $false )
| ( ( in @ SV82 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(532,plain,
! [SV57: $i,SV27: $i,SV83: $i,SV18: $i > $i > $o] :
( ( ( SV18 @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV83 )
= $true )
| ( ( in @ SV83 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(533,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV83: $i] :
( ( ( in @ ( sK7_Xy @ SV83 @ SV27 @ SV18 ) @ SV27 )
= $true )
| ( ( in @ SV83 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $true )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(534,plain,
! [SV57: $i,SV27: $i,SV85: $i,SV90: $i,SV18: $i > $i > $o] :
( ( ( SV18 @ SV90 @ SV85 )
= $false )
| ( ( ~ ( in @ SV90 @ SV27 ) )
= $true )
| ( ( in @ SV85 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(535,plain,
! [SV57: $i,SV27: $i,SV86: $i,SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV86 ) )
= $false )
| ( ( in @ SV86 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(536,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV86: $i] :
( ( ( ~ ( in @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV27 ) )
= $false )
| ( ( in @ SV86 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(537,plain,
! [SV71: $i,SV15: $i,SV49: $i,SV81: $i,SV91: $i] :
( ( ( in @ SV91 @ SV81 )
= $false )
| ( ( in @ SV91 @ ( sK13_SY205 @ SV49 @ SV15 ) )
= $true )
| ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV81 )
= $true )
| ( ( in @ SV81 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(538,plain,
! [SV71: $i,SV15: $i,SV49: $i,SV89: $i] :
( ( ( in @ SV89 @ SV49 )
= $false )
| ( ( in @ SV89 @ ( sK13_SY205 @ SV49 @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ SV71 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(539,plain,
! [SV75: $i,SV15: $i,SV49: $i,SV84: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ SV84 ) )
= $true )
| ( ( in @ SV93 @ ( sK13_SY205 @ SV49 @ SV15 ) )
= $true )
| ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV84 )
= $true )
| ( ( in @ SV84 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(540,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( in @ ( sK13_SY205 @ SV49 @ SV15 ) @ ( sK11_B @ SV15 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(541,plain,
! [SV75: $i,SV15: $i,SV49: $i] :
( ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV49 )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(542,plain,
! [SV75: $i,SV15: $i,SV49: $i,SV92: $i] :
( ( ( in @ SV92 @ ( sK13_SY205 @ SV49 @ SV15 ) )
= $false )
| ( ( ~ ( in @ SV92 @ SV49 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(543,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) )
= $false )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(544,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( ~ ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) ) )
= $false )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(545,plain,
! [SV57: $i,SV85: $i,SV18: $i > $i > $o,SV27: $i,SV90: $i] :
( ( ( in @ SV90 @ SV27 )
= $false )
| ( ( SV18 @ SV90 @ SV85 )
= $false )
| ( ( in @ SV85 @ ( sK6_B @ SV27 @ SV18 ) )
= $true )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(546,plain,
! [SV57: $i,SV27: $i,SV86: $i,SV18: $i > $i > $o] :
( ( ( SV18 @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV86 )
= $true )
| ( ( in @ SV86 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(547,plain,
! [SV57: $i,SV18: $i > $i > $o,SV27: $i,SV86: $i] :
( ( ( in @ ( sK7_Xy @ SV86 @ SV27 @ SV18 ) @ SV27 )
= $true )
| ( ( in @ SV86 @ ( sK6_B @ SV27 @ SV18 ) )
= $false )
| ( ( SV57
= ( sK9_SY200 @ SV57 @ SV27 @ SV18 ) )
= $false )
| ( ( SV18 @ ( sK8_SY21 @ SV27 @ SV18 ) @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(548,plain,
! [SV75: $i,SV15: $i,SV49: $i,SV84: $i,SV93: $i] :
( ( ( in @ SV93 @ SV84 )
= $false )
| ( ( in @ SV93 @ ( sK13_SY205 @ SV49 @ SV15 ) )
= $true )
| ( ( in @ ( sK14_SY219 @ SV49 @ SV15 ) @ SV84 )
= $true )
| ( ( in @ SV84 @ ( sK11_B @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(549,plain,
! [SV75: $i,SV15: $i,SV49: $i,SV92: $i] :
( ( ( in @ SV92 @ SV49 )
= $false )
| ( ( in @ SV92 @ ( sK13_SY205 @ SV49 @ SV15 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV49 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ SV75 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(550,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
= $true )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(551,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
| ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
= $true )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(552,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( ~ ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
= $true )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(553,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
= $true )
| ( ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
= $true )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(554,plain,
! [SV15: $i,SV76: $i,SV73: $i] :
( ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
= $false )
| ( ( ~ ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) ) )
= $true )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(555,plain,
! [SV15: $i,SV73: $i,SV76: $i] :
( ( ( in @ SV76 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
= $false )
| ( ( in @ SV73 @ ( sK12_SY218 @ SV76 @ SV73 @ SV15 ) )
= $false )
| ( ( SV73 = SV76 )
= $true )
| ( ( in @ SV73 @ SV15 )
= $false )
| ( ( in @ SV76 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(556,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[73,555,553,549,548,547,546,545,541,540,538,537,533,532,531,524,523,515,514,465,455,454,453,445,431,419,418,413,407,402,397,396,394,393,385,383,379,378,368,359,358,357,356,355,348,342,331,330,324,302,300,290,287,263,233,209,208,206,184,183,182,181,180,179,158,133,124,123,122,121]) ).
thf(557,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU509^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n011.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 15:26:36 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.47/0.48
% 1.47/0.48 No.of.Axioms: 0
% 1.47/0.48
% 1.47/0.48 Length.of.Defs: 5910
% 1.47/0.48
% 1.47/0.48 Contains.Choice.Funs: true
% 1.47/0.48 .......................
% 1.47/0.48
% 1.47/0.48 ********************************
% 1.47/0.48 * All subproblems solved! *
% 1.47/0.48 ********************************
% 1.47/0.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:25,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:556,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.47/0.48
% 1.47/0.48 %**** Beginning of derivation protocol ****
% 1.47/0.48 % SZS output start CNFRefutation
% See solution above
% 1.47/0.49
% 1.47/0.49 %**** End of derivation protocol ****
% 1.47/0.49 %**** no. of clauses in derivation: 557 ****
% 1.47/0.49 %**** clause counter: 556 ****
% 1.47/0.49
% 1.47/0.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:25,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:556,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------