%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU503^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:38 AM UTC 2026
% Result : Theorem 1.05s 0.39s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 22
% Syntax : Number of formulae : 566 ( 161 unt; 0 typ; 21 def)
% Number of atoms : 5306 (1608 equ; 0 cnn)
% Maximal formula atoms : 20 ( 9 avg)
% Number of connectives : 13422 (3327 ~;2163 |; 78 &;7639 @)
% ( 24 <=>; 191 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 309 ( 309 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 24 con; 0-4 aty)
% Number of variables : 2409 ( 73 ^;2278 !; 58 ?;2409 :)
% 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_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_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $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_SY260,type,
sK10_SY260: $i > ( $i > $o ) > $i ).
thf(tp_sK11_SY261,type,
sK11_SY261: $i > ( $i > $o ) > $i ).
thf(tp_sK12_SY262,type,
sK12_SY262: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK13_SY263,type,
sK13_SY263: $i > $i > $i ).
thf(tp_sK14_SY197,type,
sK14_SY197: $i > ( $i > $o ) > $i ).
thf(tp_sK15_SY197,type,
sK15_SY197: $i > ( $i > $o ) > $i ).
thf(tp_sK16_SY222,type,
sK16_SY222: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK17_SY274,type,
sK17_SY274: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK18_SY222,type,
sK18_SY222: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK19_SY265,type,
sK19_SY265: $i > $i > $i > $i ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK20_SY265,type,
sK20_SY265: $i > $i > $i > $i ).
thf(tp_sK21_SY285,type,
sK21_SY285: $i > $i > $i > $i ).
thf(tp_sK22_SY297,type,
sK22_SY297: $i > $i > $i > $i ).
thf(tp_sK23_SY301,type,
sK23_SY301: $i > $i > $i > $i ).
thf(tp_sK24_SY293,type,
sK24_SY293: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK25_SY295,type,
sK25_SY295: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK2_SY177,type,
sK2_SY177: $i > $i ).
thf(tp_sK3_SY216,type,
sK3_SY216: $i > $i > $i ).
thf(tp_sK4_SY219,type,
sK4_SY219: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK5_SY175,type,
sK5_SY175: $i > $i ).
thf(tp_sK6_SY200,type,
sK6_SY200: $i > $i > $i ).
thf(tp_sK7_SY237,type,
sK7_SY237: $i > $i > $i ).
thf(tp_sK8_SY222,type,
sK8_SY222: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK9_SY226,type,
sK9_SY226: $i > $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $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/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(prop2set,definition,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(2,negated_conjecture,
( ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
=> ( ! [SY18: $i > $i > $o,SY19: $i] :
( ! [SY20: $i] :
( ( in @ SY20 @ SY19 )
=> ? [SY22: $i] :
( ( SY18 @ SY20 @ SY22 )
& ! [SY23: $i] :
( ( SY18 @ SY20 @ SY23 )
=> ( SY22 = SY23 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY19 )
& ( SY18 @ 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 ) ) ) ) ) )
=> ( ! [SY50: $i > $o] :
( ? [SY52: $i] :
( ( SY50 @ SY52 )
& ! [SY53: $i] :
( ( SY50 @ SY53 )
=> ( SY52 = SY53 ) ) )
=> ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ 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 ) )
=> ( ! [SY67: $i > $o] :
( ? [SY69: $i] :
( ( SY67 @ SY69 )
& ! [SY70: $i] :
( ( SY67 @ SY70 )
=> ( SY69 = SY70 ) ) )
=> ? [Xx: $i] :
( ( SY67 @ Xx )
& ! [Xy: $i] :
( ( SY67 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY73: $o,SY74: $i] :
( ( in @ SY74
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY75: $i] : SY73 ) )
=> SY73 )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,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,
( ( ! [SY18: $i > $i > $o,SY19: $i] :
( ! [SY20: $i] :
( ( in @ SY20 @ SY19 )
=> ? [SY22: $i] :
( ( SY18 @ SY20 @ SY22 )
& ! [SY23: $i] :
( ( SY18 @ SY20 @ SY23 )
=> ( SY22 = SY23 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY19 )
& ( SY18 @ 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,
( ( ! [SY50: $i > $o] :
( ? [SY52: $i] :
( ( SY50 @ SY52 )
& ! [SY53: $i] :
( ( SY50 @ SY53 )
=> ( SY52 = SY53 ) ) )
=> ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ 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,
( ( ! [SY67: $i > $o] :
( ? [SY69: $i] :
( ( SY67 @ SY69 )
& ! [SY70: $i] :
( ( SY67 @ SY70 )
=> ( SY69 = SY70 ) ) )
=> ? [Xx: $i] :
( ( SY67 @ Xx )
& ! [Xy: $i] :
( ( SY67 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [SY73: $o,SY74: $i] :
( ( in @ SY74
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY75: $i] : SY73 ) )
=> SY73 ) )
= $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 ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ~ ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [SY73: $o,SY74: $i] :
( ( in @ SY74
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY75: $i] : SY73 ) )
=> SY73 ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(28,plain,
( ( ! [SY67: $i > $o] :
( ? [SY69: $i] :
( ( SY67 @ SY69 )
& ! [SY70: $i] :
( ( SY67 @ SY70 )
=> ( SY69 = SY70 ) ) )
=> ? [Xx: $i] :
( ( SY67 @ Xx )
& ! [Xy: $i] :
( ( SY67 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(29,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(30,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(31,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(32,plain,
( ( ! [SY50: $i > $o] :
( ? [SY52: $i] :
( ( SY50 @ SY52 )
& ! [SY53: $i] :
( ( SY50 @ SY53 )
=> ( SY52 = SY53 ) ) )
=> ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(33,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(34,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(35,plain,
( ( ! [SY18: $i > $i > $o,SY19: $i] :
( ! [SY20: $i] :
( ( in @ SY20 @ SY19 )
=> ? [SY22: $i] :
( ( SY18 @ SY20 @ SY22 )
& ! [SY23: $i] :
( ( SY18 @ SY20 @ SY23 )
=> ( SY22 = SY23 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY19 )
& ( SY18 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(37,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(38,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(39,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(41,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(42,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(44,plain,
( ( ~ ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(46,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(47,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( SX0 @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( SX0 @ SX2 @ SX4 )
| ( SX3 = SX4 ) ) ) )
| ~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) )
| ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(48,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(49,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[26,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(50,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(51,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( in @ emptyset @ SX0 )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ( in @ SX1 @ omega )
| ~ ( in @ SX1 @ SX0 ) )
| ( in @ ( setadjoin @ SX1 @ SX1 ) @ SX0 ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(52,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(53,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX4 )
| ( in @ SX3 @ SX4 ) )
| ~ ( ~ ( in @ SX3 @ SX4 )
| ( in @ SX2 @ SX4 ) ) ) )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX2 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SX2 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(54,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(55,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(57,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX2: $i] : SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[27,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(59,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(60,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[25,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(61,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(62,plain,
! [SV1: $i] :
( ( ~ ( in @ SV1 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(63,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(64,plain,
! [SV2: $i] :
( ( ! [SY156: $i] :
( ~ ! [SY157: $i] :
~ ( ~ ( ~ ( in @ SY157 @ SV2 )
| ( in @ SY157 @ SY156 ) )
| ~ ( ~ ( in @ SY157 @ SY156 )
| ( in @ SY157 @ SV2 ) ) )
| ( SV2 = SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(65,plain,
! [SV3: $i] :
( ( ! [SY158: $i > $o,SY159: $i] :
( ~ ( in @ SY159
@ ( dsetconstr @ SV3
@ ^ [SX3: $i] : ( SY158 @ SX3 ) ) )
| ( SY158 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(66,plain,
! [SV4: $i > $i > $o] :
( ( ! [SY161: $i] :
( ~ ! [SY162: $i] :
( ~ ( in @ SY162 @ SY161 )
| ~ ! [SY163: $i] :
~ ~ ( ~ ( SV4 @ SY162 @ SY163 )
| ~ ! [SY164: $i] :
( ~ ( SV4 @ SY162 @ SY164 )
| ( SY163 = SY164 ) ) ) )
| ~ ! [SY165: $i] :
~ ! [SY166: $i] :
~ ( ~ ( ~ ( in @ SY166 @ SY165 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY167 @ SY161 )
| ~ ( SV4 @ SY167 @ SY166 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY168 @ SY161 )
| ~ ( SV4 @ SY168 @ SY166 ) )
| ( in @ SY166 @ SY165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(67,plain,
! [SV5: $i] :
( ( ! [SY169: $i] :
~ ( ~ ( ~ ( in @ SY169 @ ( setunion @ SV5 ) )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( in @ SY169 @ SY170 )
| ~ ( in @ SY170 @ SV5 ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( in @ SY169 @ SY171 )
| ~ ( in @ SY171 @ SV5 ) )
| ( in @ SY169 @ ( setunion @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(68,plain,
! [SV6: $i] :
( ( ~ ( in @ SV6 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(69,plain,
! [SV7: $i] :
( ( ! [SY173: $i,SY174: $i] :
~ ( ~ ( ~ ( in @ SY174 @ ( setadjoin @ SV7 @ SY173 ) )
| ( SY174 = SV7 )
| ( in @ SY174 @ SY173 ) )
| ~ ( ~ ( ( SY174 = SV7 )
| ( in @ SY174 @ SY173 ) )
| ( in @ SY174 @ ( setadjoin @ SV7 @ SY173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(70,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV8 )
| ~ ! [SY175: $i] :
( ~ ~ ( ~ ( in @ SY175 @ omega )
| ~ ( in @ SY175 @ SV8 ) )
| ( in @ ( setadjoin @ SY175 @ SY175 ) @ SV8 ) ) )
| ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(71,plain,
! [SV9: $i] :
( ( ~ ( in @ SV9 @ omega )
| ( in @ ( setadjoin @ SV9 @ SV9 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(72,plain,
! [SV10: $i] :
( ( ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY178: $i] :
( ~ ( in @ SY178 @ SY177 )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY178 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY180: $i,SY181: $i] :
( ~ ~ ( ~ ( in @ SY180 @ SV10 )
| ~ ( in @ SY181 @ SV10 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY177 )
| ~ ( ~ ( ~ ( in @ SY180 @ SX4 )
| ( in @ SY181 @ SX4 ) )
| ~ ( ~ ( in @ SY181 @ SX4 )
| ( in @ SY180 @ SX4 ) ) ) )
| ( SY180 = SY181 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY177 )
| ~ ( in @ SX3 @ SY177 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY187: $i] :
( ~ ~ ( ~ ! [SY188: $i] :
( ~ ( in @ SY188 @ SY187 )
| ( in @ SY188 @ SV10 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY187 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY177 )
| ~ ( in @ SX4 @ SY187 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY187 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY177 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(73,plain,
! [SV11: $i > $o] :
( ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ( SV11 @ SY195 )
| ~ ! [SY196: $i] :
( ~ ( SV11 @ SY196 )
| ( SY195 = SY196 ) ) )
| ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(74,plain,
! [SV12: $i] :
( ( ~ ~ ! [SY199: $i] :
~ ( in @ SY199 @ SV12 )
| ~ ! [SY200: $i] :
~ ~ ( ~ ( in @ SY200 @ SV12 )
| ~ ~ ~ ! [SY201: $i] :
~ ~ ( ~ ( in @ SY201 @ SY200 )
| ~ ( in @ SY201 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(75,plain,
! [SV13: $i] :
( ( ! [SY202: $i > $o,SY203: $i] :
( ~ ( in @ SY203 @ SV13 )
| ~ ( SY202 @ SY203 )
| ( in @ SY203
@ ( dsetconstr @ SV13
@ ^ [SX3: $i] : ( SY202 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(76,plain,
! [SV14: $o] :
( ( ! [SY205: $i] :
( ~ ( in @ SY205
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY206: $i] : SV14 ) )
| SV14 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[57]) ).
thf(77,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[57]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[57]) ).
thf(79,plain,
! [SV15: $i] :
( ( ! [SY207: $i > $o,SY208: $i] :
( ~ ( in @ SY208
@ ( dsetconstr @ SV15
@ ^ [SX3: $i] : ( SY207 @ SX3 ) ) )
| ( in @ SY208 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(80,plain,
! [SV16: $i] :
( ( ! [SY210: $i] :
~ ( ~ ( ~ ( in @ SY210 @ ( powerset @ SV16 ) )
| ! [SY211: $i] :
( ~ ( in @ SY211 @ SY210 )
| ( in @ SY211 @ SV16 ) ) )
| ~ ( ~ ! [SY212: $i] :
( ~ ( in @ SY212 @ SY210 )
| ( in @ SY212 @ SV16 ) )
| ( in @ SY210 @ ( powerset @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(81,plain,
! [SV17: $i] :
( ( ~ ( in @ SV17 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(82,plain,
! [SV18: $i > $o] :
( ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( SV18 @ SY213 )
| ~ ! [SY214: $i] :
( ~ ( SV18 @ SY214 )
| ( SY213 = SY214 ) ) )
| ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(83,plain,
! [SV1: $i] :
( ( in @ SV1 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(84,plain,
( ( ~ ( in @ sK1_Xx @ emptyset ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(85,plain,
! [SV19: $i,SV2: $i] :
( ( ~ ! [SY216: $i] :
~ ( ~ ( ~ ( in @ SY216 @ SV2 )
| ( in @ SY216 @ SV19 ) )
| ~ ( ~ ( in @ SY216 @ SV19 )
| ( in @ SY216 @ SV2 ) ) )
| ( SV2 = SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(86,plain,
! [SV20: $i > $o,SV3: $i] :
( ( ! [SY217: $i] :
( ~ ( in @ SY217
@ ( dsetconstr @ SV3
@ ^ [SY218: $i] : ( SV20 @ SY218 ) ) )
| ( SV20 @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(87,plain,
! [SV4: $i > $i > $o,SV21: $i] :
( ( ~ ! [SY219: $i] :
( ~ ( in @ SY219 @ SV21 )
| ~ ! [SY163: $i] :
~ ~ ( ~ ( SV4 @ SY219 @ SY163 )
| ~ ! [SY164: $i] :
( ~ ( SV4 @ SY219 @ SY164 )
| ( SY163 = SY164 ) ) ) )
| ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( in @ SV22 @ ( setunion @ SV5 ) )
| ~ ! [SY226: $i] :
~ ~ ( ~ ( in @ SV22 @ SY226 )
| ~ ( in @ SY226 @ SV5 ) ) )
| ~ ( ~ ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV22 @ SY227 )
| ~ ( in @ SY227 @ SV5 ) )
| ( in @ SV22 @ ( setunion @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV6: $i] :
( ( ( ~ ( in @ SV6 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(90,plain,
! [SV23: $i,SV7: $i] :
( ( ! [SY228: $i] :
~ ( ~ ( ~ ( in @ SY228 @ ( setadjoin @ SV7 @ SV23 ) )
| ( SY228 = SV7 )
| ( in @ SY228 @ SV23 ) )
| ~ ( ~ ( ( SY228 = SV7 )
| ( in @ SY228 @ SV23 ) )
| ( in @ SY228 @ ( setadjoin @ SV7 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV8 )
| ~ ! [SY175: $i] :
( ~ ~ ( ~ ( in @ SY175 @ omega )
| ~ ( in @ SY175 @ SV8 ) )
| ( in @ ( setadjoin @ SY175 @ SY175 ) @ SV8 ) ) ) )
= $true )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(92,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV9 @ SV9 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV10: $i] :
( ( ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY178: $i] :
( ~ ( in @ SY178 @ SY177 )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY178 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY180: $i,SY181: $i] :
( ~ ~ ( ~ ( in @ SY180 @ SV10 )
| ~ ( in @ SY181 @ SV10 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY177 )
| ~ ( ~ ( ~ ( in @ SY180 @ SX4 )
| ( in @ SY181 @ SX4 ) )
| ~ ( ~ ( in @ SY181 @ SX4 )
| ( in @ SY180 @ SX4 ) ) ) )
| ( SY180 = SY181 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY177 )
| ~ ( in @ SX3 @ SY177 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY187: $i] :
( ~ ~ ( ~ ! [SY188: $i] :
( ~ ( in @ SY188 @ SY187 )
| ( in @ SY188 @ SV10 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY187 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY177 )
| ~ ( in @ SX4 @ SY187 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY187 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY177 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV11: $i > $o] :
( ( ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ( SV11 @ SY195 )
| ~ ! [SY196: $i] :
( ~ ( SV11 @ SY196 )
| ( SY195 = SY196 ) ) ) )
= $true )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV12: $i] :
( ( ( ~ ~ ! [SY199: $i] :
~ ( in @ SY199 @ SV12 ) )
= $true )
| ( ( ~ ! [SY200: $i] :
~ ~ ( ~ ( in @ SY200 @ SV12 )
| ~ ~ ~ ! [SY201: $i] :
~ ~ ( ~ ( in @ SY201 @ SY200 )
| ~ ( in @ SY201 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV24: $i > $o,SV13: $i] :
( ( ! [SY229: $i] :
( ~ ( in @ SY229 @ SV13 )
| ~ ( SV24 @ SY229 )
| ( in @ SY229
@ ( dsetconstr @ SV13
@ ^ [SY230: $i] : ( SV24 @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV14: $o,SV25: $i] :
( ( ~ ( in @ SV25
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY206: $i] : SV14 ) )
| SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV26: $i] :
( ( ~ ( in @ SV26
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
! [SV27: $i] :
( ( ~ ( in @ SV27
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV28: $i > $o,SV15: $i] :
( ( ! [SY234: $i] :
( ~ ( in @ SY234
@ ( dsetconstr @ SV15
@ ^ [SY235: $i] : ( SV28 @ SY235 ) ) )
| ( in @ SY234 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
! [SV16: $i,SV29: $i] :
( ( ~ ( ~ ( ~ ( in @ SV29 @ ( powerset @ SV16 ) )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV29 )
| ( in @ SY236 @ SV16 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV29 )
| ( in @ SY237 @ SV16 ) )
| ( in @ SV29 @ ( powerset @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(102,plain,
! [SV17: $i] :
( ( ( ~ ( in @ SV17 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV18: $i > $o] :
( ( ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( SV18 @ SY213 )
| ~ ! [SY214: $i] :
( ~ ( SV18 @ SY214 )
| ( SY213 = SY214 ) ) ) )
= $true )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(104,plain,
( ( in @ sK1_Xx @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(105,plain,
! [SV19: $i,SV2: $i] :
( ( ( ~ ! [SY216: $i] :
~ ( ~ ( ~ ( in @ SY216 @ SV2 )
| ( in @ SY216 @ SV19 ) )
| ~ ( ~ ( in @ SY216 @ SV19 )
| ( in @ SY216 @ SV2 ) ) ) )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(106,plain,
! [SV20: $i > $o,SV3: $i,SV30: $i] :
( ( ~ ( in @ SV30
@ ( dsetconstr @ SV3
@ ^ [SY218: $i] : ( SV20 @ SY218 ) ) )
| ( SV20 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(107,plain,
! [SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ! [SY219: $i] :
( ~ ( in @ SY219 @ SV21 )
| ~ ! [SY163: $i] :
~ ~ ( ~ ( SV4 @ SY219 @ SY163 )
| ~ ! [SY164: $i] :
( ~ ( SV4 @ SY219 @ SY164 )
| ( SY163 = SY164 ) ) ) ) )
= $true )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(108,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ( ~ ( in @ SV22 @ ( setunion @ SV5 ) )
| ~ ! [SY226: $i] :
~ ~ ( ~ ( in @ SV22 @ SY226 )
| ~ ( in @ SY226 @ SV5 ) ) )
| ~ ( ~ ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV22 @ SY227 )
| ~ ( in @ SY227 @ SV5 ) )
| ( in @ SV22 @ ( setunion @ SV5 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(109,plain,
! [SV6: $i] :
( ( ( in @ SV6 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(110,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
| ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
| ~ ( ~ ( ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
| ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(111,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV8 )
| ~ ! [SY175: $i] :
( ~ ~ ( ~ ( in @ SY175 @ omega )
| ~ ( in @ SY175 @ SV8 ) )
| ( in @ ( setadjoin @ SY175 @ SY175 ) @ SV8 ) ) ) )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(112,plain,
! [SV9: $i] :
( ( ( in @ SV9 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV9 @ SV9 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(113,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) )
| ~ ! [SY244: $i,SY245: $i] :
( ~ ~ ( ~ ( in @ SY244 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY245 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY244 )
| ( in @ SX4 @ SY245 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY245 )
| ( in @ SX4 @ SY244 ) ) ) )
| ~ ! [SY248: $i] :
( ~ ~ ( ~ ! [SY188: $i] :
( ~ ( in @ SY188 @ SY248 )
| ( in @ SY188 @ SV10 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY248 ) )
| ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY252 @ SY248 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY251 )
| ~ ( in @ SX5 @ SY248 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY254 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[93]) ).
thf(114,plain,
! [SV11: $i > $o] :
( ( ( ~ ! [SY195: $i] :
~ ~ ( ~ ( SV11 @ SY195 )
| ~ ! [SY196: $i] :
( ~ ( SV11 @ SY196 )
| ( SY195 = SY196 ) ) ) )
= $false )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(115,plain,
! [SV12: $i] :
( ( ( ~ ! [SY199: $i] :
~ ( in @ SY199 @ SV12 ) )
= $false )
| ( ( ~ ! [SY200: $i] :
~ ~ ( ~ ( in @ SY200 @ SV12 )
| ~ ~ ~ ! [SY201: $i] :
~ ~ ( ~ ( in @ SY201 @ SY200 )
| ~ ( in @ SY201 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(116,plain,
! [SV24: $i > $o,SV13: $i,SV32: $i] :
( ( ~ ( in @ SV32 @ SV13 )
| ~ ( SV24 @ SV32 )
| ( in @ SV32
@ ( dsetconstr @ SV13
@ ^ [SY230: $i] : ( SV24 @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(117,plain,
! [SV14: $o,SV25: $i] :
( ( ( ~ ( in @ SV25
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY206: $i] : SV14 ) ) )
= $true )
| ( SV14 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(118,plain,
! [SV26: $i] :
( ( ( ~ ( in @ SV26
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(119,plain,
! [SV27: $i] :
( ( ( ~ ( in @ SV27
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(120,plain,
! [SV28: $i > $o,SV15: $i,SV33: $i] :
( ( ~ ( in @ SV33
@ ( dsetconstr @ SV15
@ ^ [SY235: $i] : ( SV28 @ SY235 ) ) )
| ( in @ SV33 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(121,plain,
! [SV16: $i,SV29: $i] :
( ( ~ ( ~ ( in @ SV29 @ ( powerset @ SV16 ) )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV29 )
| ( in @ SY236 @ SV16 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV29 )
| ( in @ SY237 @ SV16 ) )
| ( in @ SV29 @ ( powerset @ SV16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(122,plain,
! [SV17: $i] :
( ( ( in @ SV17 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(123,plain,
! [SV18: $i > $o] :
( ( ( ~ ! [SY213: $i] :
~ ~ ( ~ ( SV18 @ SY213 )
| ~ ! [SY214: $i] :
( ~ ( SV18 @ SY214 )
| ( SY213 = SY214 ) ) ) )
= $false )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(124,plain,
! [SV19: $i,SV2: $i] :
( ( ( ! [SY216: $i] :
~ ( ~ ( ~ ( in @ SY216 @ SV2 )
| ( in @ SY216 @ SV19 ) )
| ~ ( ~ ( in @ SY216 @ SV19 )
| ( in @ SY216 @ SV2 ) ) ) )
= $false )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(125,plain,
! [SV20: $i > $o,SV3: $i,SV30: $i] :
( ( ( ~ ( in @ SV30
@ ( dsetconstr @ SV3
@ ^ [SY218: $i] : ( SV20 @ SY218 ) ) ) )
= $true )
| ( ( SV20 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(126,plain,
! [SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY219: $i] :
( ~ ( in @ SY219 @ SV21 )
| ~ ! [SY163: $i] :
~ ~ ( ~ ( SV4 @ SY219 @ SY163 )
| ~ ! [SY164: $i] :
( ~ ( SV4 @ SY219 @ SY164 )
| ( SY163 = SY164 ) ) ) ) )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(127,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ( ~ ( in @ SV22 @ ( setunion @ SV5 ) )
| ~ ! [SY226: $i] :
~ ~ ( ~ ( in @ SV22 @ SY226 )
| ~ ( in @ SY226 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(128,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ( ~ ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV22 @ SY227 )
| ~ ( in @ SY227 @ SV5 ) )
| ( in @ SV22 @ ( setunion @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(129,plain,
! [SV6: $i,SV34: $o] :
( ( SV34 = $true )
| ( ( in @ SV6 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[109]) ).
thf(130,plain,
! [SV6: $i] :
( ( $true = $true )
| ( ( in @ SV6 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[109]) ).
thf(131,plain,
! [SV6: $i] :
( ( $false = $true )
| ( ( in @ SV6 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[109]) ).
thf(132,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ~ ( ~ ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
| ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
| ~ ( ~ ( ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
| ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(133,plain,
! [SV8: $i] :
( ( ( ~ ( in @ emptyset @ SV8 )
| ~ ! [SY175: $i] :
( ~ ~ ( ~ ( in @ SY175 @ omega )
| ~ ( in @ SY175 @ SV8 ) )
| ( in @ ( setadjoin @ SY175 @ SY175 ) @ SV8 ) ) )
= $true )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(134,plain,
! [SV10: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) )
| ~ ! [SY244: $i,SY245: $i] :
( ~ ~ ( ~ ( in @ SY244 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY245 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY244 )
| ( in @ SX4 @ SY245 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY245 )
| ( in @ SX4 @ SY244 ) ) ) )
| ~ ! [SY248: $i] :
( ~ ~ ( ~ ! [SY188: $i] :
( ~ ( in @ SY188 @ SY248 )
| ( in @ SY188 @ SV10 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY248 ) )
| ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY252 @ SY248 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY251 )
| ~ ( in @ SX5 @ SY248 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY254 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(135,plain,
! [SV11: $i > $o] :
( ( ( ! [SY195: $i] :
~ ~ ( ~ ( SV11 @ SY195 )
| ~ ! [SY196: $i] :
( ~ ( SV11 @ SY196 )
| ( SY195 = SY196 ) ) ) )
= $true )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(136,plain,
! [SV12: $i] :
( ( ( ! [SY199: $i] :
~ ( in @ SY199 @ SV12 ) )
= $true )
| ( ( ~ ! [SY200: $i] :
~ ~ ( ~ ( in @ SY200 @ SV12 )
| ~ ~ ~ ! [SY201: $i] :
~ ~ ( ~ ( in @ SY201 @ SY200 )
| ~ ( in @ SY201 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(137,plain,
! [SV24: $i > $o,SV13: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV13 ) )
= $true )
| ( ( ~ ( SV24 @ SV32 )
| ( in @ SV32
@ ( dsetconstr @ SV13
@ ^ [SY230: $i] : ( SV24 @ SY230 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(138,plain,
! [SV14: $o,SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY206: $i] : SV14 ) )
= $false )
| ( SV14 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(139,plain,
! [SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(140,plain,
! [SV27: $i] :
( ( ( in @ SV27
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(141,plain,
! [SV28: $i > $o,SV15: $i,SV33: $i] :
( ( ( ~ ( in @ SV33
@ ( dsetconstr @ SV15
@ ^ [SY235: $i] : ( SV28 @ SY235 ) ) ) )
= $true )
| ( ( in @ SV33 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(142,plain,
! [SV16: $i,SV29: $i] :
( ( ~ ( ~ ( in @ SV29 @ ( powerset @ SV16 ) )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV29 )
| ( in @ SY236 @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(143,plain,
! [SV16: $i,SV29: $i] :
( ( ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV29 )
| ( in @ SY237 @ SV16 ) )
| ( in @ SV29 @ ( powerset @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(144,plain,
! [SV18: $i > $o] :
( ( ( ! [SY213: $i] :
~ ~ ( ~ ( SV18 @ SY213 )
| ~ ! [SY214: $i] :
( ~ ( SV18 @ SY214 )
| ( SY213 = SY214 ) ) ) )
= $true )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(145,plain,
! [SV2: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 ) )
| ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) ) ) )
= $false )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[124]) ).
thf(146,plain,
! [SV20: $i > $o,SV3: $i,SV30: $i] :
( ( ( in @ SV30
@ ( dsetconstr @ SV3
@ ^ [SY218: $i] : ( SV20 @ SY218 ) ) )
= $false )
| ( ( SV20 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(147,plain,
! [SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
| ~ ! [SY258: $i] :
~ ~ ( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY258 )
| ~ ! [SY259: $i] :
( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY259 )
| ( SY258 = SY259 ) ) ) )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[126]) ).
thf(148,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ( in @ SV22 @ ( setunion @ SV5 ) )
| ~ ! [SY226: $i] :
~ ~ ( ~ ( in @ SV22 @ SY226 )
| ~ ( in @ SY226 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(149,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV22 @ SY227 )
| ~ ( in @ SY227 @ SV5 ) )
| ( in @ SV22 @ ( setunion @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(150,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ~ ( ~ ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
| ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(151,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ~ ( ~ ( ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
| ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(152,plain,
! [SV8: $i] :
( ( ( ~ ( in @ emptyset @ SV8 ) )
= $true )
| ( ( ~ ! [SY175: $i] :
( ~ ~ ( ~ ( in @ SY175 @ omega )
| ~ ( in @ SY175 @ SV8 ) )
| ( in @ ( setadjoin @ SY175 @ SY175 ) @ SV8 ) ) )
= $true )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(153,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) )
| ~ ! [SY244: $i,SY245: $i] :
( ~ ~ ( ~ ( in @ SY244 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY245 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY244 )
| ( in @ SX4 @ SY245 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY245 )
| ( in @ SX4 @ SY244 ) ) ) )
| ~ ! [SY248: $i] :
( ~ ~ ( ~ ! [SY188: $i] :
( ~ ( in @ SY188 @ SY248 )
| ( in @ SY188 @ SV10 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY248 ) )
| ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY252 @ SY248 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY251 )
| ~ ( in @ SX5 @ SY248 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY254 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(154,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ~ ( ~ ( SV11 @ SV35 )
| ~ ! [SY260: $i] :
( ~ ( SV11 @ SY260 )
| ( SV35 = SY260 ) ) ) )
= $true )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV12: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ SV12 ) )
= $true )
| ( ( ~ ! [SY200: $i] :
~ ~ ( ~ ( in @ SY200 @ SV12 )
| ~ ~ ~ ! [SY201: $i] :
~ ~ ( ~ ( in @ SY201 @ SY200 )
| ~ ( in @ SY201 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV24: $i > $o,SV13: $i,SV32: $i] :
( ( ( in @ SV32 @ SV13 )
= $false )
| ( ( ~ ( SV24 @ SV32 )
| ( in @ SV32
@ ( dsetconstr @ SV13
@ ^ [SY230: $i] : ( SV24 @ SY230 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV28: $i > $o,SV15: $i,SV33: $i] :
( ( ( in @ SV33
@ ( dsetconstr @ SV15
@ ^ [SY235: $i] : ( SV28 @ SY235 ) ) )
= $false )
| ( ( in @ SV33 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(158,plain,
! [SV16: $i,SV29: $i] :
( ( ~ ( in @ SV29 @ ( powerset @ SV16 ) )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV29 )
| ( in @ SY236 @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(159,plain,
! [SV16: $i,SV29: $i] :
( ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV29 )
| ( in @ SY237 @ SV16 ) )
| ( in @ SV29 @ ( powerset @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(160,plain,
! [SV37: $i,SV18: $i > $o] :
( ( ( ~ ~ ( ~ ( SV18 @ SV37 )
| ~ ! [SY261: $i] :
( ~ ( SV18 @ SY261 )
| ( SV37 = SY261 ) ) ) )
= $true )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(161,plain,
! [SV2: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 ) )
| ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(162,plain,
! [SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 ) )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(163,plain,
! [SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ! [SY258: $i] :
~ ~ ( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY258 )
| ~ ! [SY259: $i] :
( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY259 )
| ( SY258 = SY259 ) ) ) )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(164,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( setunion @ SV5 ) ) )
= $true )
| ( ( ~ ! [SY226: $i] :
~ ~ ( ~ ( in @ SV22 @ SY226 )
| ~ ( in @ SY226 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(165,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV22 @ SY227 )
| ~ ( in @ SY227 @ SV5 ) ) )
= $true )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(166,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ~ ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
| ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(167,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ~ ( ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
| ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(168,plain,
! [SV8: $i] :
( ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ~ ! [SY175: $i] :
( ~ ~ ( ~ ( in @ SY175 @ omega )
| ~ ( in @ SY175 @ SV8 ) )
| ( in @ ( setadjoin @ SY175 @ SY175 ) @ SV8 ) ) )
= $true )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(169,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) )
| ~ ! [SY244: $i,SY245: $i] :
( ~ ~ ( ~ ( in @ SY244 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY245 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY244 )
| ( in @ SX4 @ SY245 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY245 )
| ( in @ SX4 @ SY244 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(170,plain,
! [SV10: $i] :
( ( ~ ! [SY248: $i] :
( ~ ~ ( ~ ! [SY188: $i] :
( ~ ( in @ SY188 @ SY248 )
| ( in @ SY188 @ SV10 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY248 ) )
| ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY252 @ SY248 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY251 )
| ~ ( in @ SX5 @ SY248 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY254 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(171,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( ~ ( SV11 @ SV35 )
| ~ ! [SY260: $i] :
( ~ ( SV11 @ SY260 )
| ( SV35 = SY260 ) ) ) )
= $false )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(172,plain,
! [SV12: $i,SV36: $i] :
( ( ( in @ SV36 @ SV12 )
= $false )
| ( ( ~ ! [SY200: $i] :
~ ~ ( ~ ( in @ SY200 @ SV12 )
| ~ ~ ~ ! [SY201: $i] :
~ ~ ( ~ ( in @ SY201 @ SY200 )
| ~ ( in @ SY201 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(173,plain,
! [SV13: $i,SV32: $i,SV24: $i > $o] :
( ( ( ~ ( SV24 @ SV32 ) )
= $true )
| ( ( in @ SV32
@ ( dsetconstr @ SV13
@ ^ [SY230: $i] : ( SV24 @ SY230 ) ) )
= $true )
| ( ( in @ SV32 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(174,plain,
! [SV16: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ ( powerset @ SV16 ) ) )
= $true )
| ( ( ! [SY236: $i] :
( ~ ( in @ SY236 @ SV29 )
| ( in @ SY236 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(175,plain,
! [SV16: $i,SV29: $i] :
( ( ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV29 )
| ( in @ SY237 @ SV16 ) ) )
= $true )
| ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(176,plain,
! [SV37: $i,SV18: $i > $o] :
( ( ( ~ ( ~ ( SV18 @ SV37 )
| ~ ! [SY261: $i] :
( ~ ( SV18 @ SY261 )
| ( SV37 = SY261 ) ) ) )
= $false )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(177,plain,
! [SV2: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(178,plain,
! [SV21: $i,SV4: $i > $i > $o] :
( ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(179,plain,
! [SV21: $i,SV4: $i > $i > $o] :
( ( ( ! [SY258: $i] :
~ ~ ( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY258 )
| ~ ! [SY259: $i] :
( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY259 )
| ( SY258 = SY259 ) ) ) )
= $true )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(180,plain,
! [SV5: $i,SV22: $i] :
( ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $false )
| ( ( ~ ! [SY226: $i] :
~ ~ ( ~ ( in @ SV22 @ SY226 )
| ~ ( in @ SY226 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(181,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV22 @ SY227 )
| ~ ( in @ SY227 @ SV5 ) ) )
= $false )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(182,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) ) )
= $true )
| ( ( ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(183,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ( ~ ( ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) ) )
= $true )
| ( ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(184,plain,
! [SV8: $i] :
( ( ( ! [SY175: $i] :
( ~ ~ ( ~ ( in @ SY175 @ omega )
| ~ ( in @ SY175 @ SV8 ) )
| ( in @ ( setadjoin @ SY175 @ SY175 ) @ SV8 ) ) )
= $false )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(185,plain,
! [SV10: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) )
| ~ ! [SY244: $i,SY245: $i] :
( ~ ~ ( ~ ( in @ SY244 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY245 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY244 )
| ( in @ SX4 @ SY245 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY245 )
| ( in @ SX4 @ SY244 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(186,plain,
! [SV10: $i] :
( ( ! [SY248: $i] :
( ~ ~ ( ~ ! [SY188: $i] :
( ~ ( in @ SY188 @ SY248 )
| ( in @ SY188 @ SV10 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY248 ) )
| ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY252 @ SY248 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY251 )
| ~ ( in @ SX5 @ SY248 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY254 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(187,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ SV35 )
| ~ ! [SY260: $i] :
( ~ ( SV11 @ SY260 )
| ( SV35 = SY260 ) ) )
= $true )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(188,plain,
! [SV36: $i,SV12: $i] :
( ( ( ! [SY200: $i] :
~ ~ ( ~ ( in @ SY200 @ SV12 )
| ~ ~ ~ ! [SY201: $i] :
~ ~ ( ~ ( in @ SY201 @ SY200 )
| ~ ( in @ SY201 @ SV12 ) ) ) )
= $false )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV13: $i,SV32: $i,SV24: $i > $o] :
( ( ( SV24 @ SV32 )
= $false )
| ( ( in @ SV32
@ ( dsetconstr @ SV13
@ ^ [SY230: $i] : ( SV24 @ SY230 ) ) )
= $true )
| ( ( in @ SV32 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV16: $i,SV29: $i] :
( ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $false )
| ( ( ! [SY236: $i] :
( ~ ( in @ SY236 @ SV29 )
| ( in @ SY236 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV16: $i,SV29: $i] :
( ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ SV29 )
| ( in @ SY237 @ SV16 ) ) )
= $false )
| ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(192,plain,
! [SV37: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ SV37 )
| ~ ! [SY261: $i] :
( ~ ( SV18 @ SY261 )
| ( SV37 = SY261 ) ) )
= $true )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(193,plain,
! [SV2: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(194,plain,
! [SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV38: $i,SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
| ~ ! [SY262: $i] :
( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY262 )
| ( SV38 = SY262 ) ) ) )
= $true )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV5: $i,SV22: $i] :
( ( ( ! [SY226: $i] :
~ ~ ( ~ ( in @ SV22 @ SY226 )
| ~ ( in @ SY226 @ SV5 ) ) )
= $false )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV5: $i,SV22: $i] :
( ( ( ! [SY227: $i] :
~ ~ ( ~ ( in @ SV22 @ SY227 )
| ~ ( in @ SY227 @ SV5 ) ) )
= $true )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(198,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
= $false )
| ( ( ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(199,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ( ( SV31 = SV7 )
| ( in @ SV31 @ SV23 ) )
= $false )
| ( ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(200,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY175 @ SV8 ) @ omega )
| ~ ( in @ ( sK5_SY175 @ SV8 ) @ SV8 ) )
| ( in @ ( setadjoin @ ( sK5_SY175 @ SV8 ) @ ( sK5_SY175 @ SV8 ) ) @ SV8 ) )
= $false )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[184]) ).
thf(201,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) )
| ~ ! [SY244: $i,SY245: $i] :
( ~ ~ ( ~ ( in @ SY244 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY245 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY244 )
| ( in @ SX4 @ SY245 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY245 )
| ( in @ SX4 @ SY244 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(202,plain,
! [SV10: $i,SV39: $i] :
( ( ~ ~ ( ~ ! [SY263: $i] :
( ~ ( in @ SY263 @ SV39 )
| ( in @ SY263 @ SV10 ) )
| ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
| ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(203,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ SV35 ) )
= $true )
| ( ( ~ ! [SY260: $i] :
( ~ ( SV11 @ SY260 )
| ( SV35 = SY260 ) ) )
= $true )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(204,plain,
! [SV12: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY200 @ SV36 @ SV12 ) @ SV12 )
| ~ ~ ~ ! [SY270: $i] :
~ ~ ( ~ ( in @ SY270 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SY270 @ SV12 ) ) ) )
= $false )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[188]) ).
thf(205,plain,
! [SV16: $i,SV29: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV29 )
| ( in @ SV40 @ SV16 ) )
= $true )
| ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(206,plain,
! [SV29: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK7_SY237 @ SV16 @ SV29 ) @ SV29 )
| ( in @ ( sK7_SY237 @ SV16 @ SV29 ) @ SV16 ) )
= $false )
| ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[191]) ).
thf(207,plain,
! [SV37: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ SV37 ) )
= $true )
| ( ( ~ ! [SY261: $i] :
( ~ ( SV18 @ SY261 )
| ( SV37 = SY261 ) ) )
= $true )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(208,plain,
! [SV2: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(209,plain,
! [SV2: $i,SV19: $i] :
( ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(210,plain,
! [SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ! [SY271: $i] :
~ ( ~ ( ~ ( in @ SY271 @ ( sK8_SY222 @ SV4 @ SV21 ) )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY271 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY271 ) )
| ( in @ SY271 @ ( sK8_SY222 @ SV4 @ SV21 ) ) ) ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[194]) ).
thf(211,plain,
! [SV38: $i,SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
| ~ ! [SY262: $i] :
( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY262 )
| ( SV38 = SY262 ) ) ) )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(212,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( in @ SV22 @ ( sK9_SY226 @ SV5 @ SV22 ) )
| ~ ( in @ ( sK9_SY226 @ SV5 @ SV22 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[196]) ).
thf(213,plain,
! [SV5: $i,SV41: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( in @ SV22 @ SV41 )
| ~ ( in @ SV41 @ SV5 ) ) )
= $true )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(214,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ( SV31 = SV7 )
= $true )
| ( ( in @ SV31 @ SV23 )
= $true )
| ( ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(215,plain,
! [SV23: $i,SV7: $i,SV31: $i] :
( ( ( SV31 = SV7 )
= $false )
| ( ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(216,plain,
! [SV7: $i,SV23: $i,SV31: $i] :
( ( ( in @ SV31 @ SV23 )
= $false )
| ( ( in @ SV31 @ ( setadjoin @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(217,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY175 @ SV8 ) @ omega )
| ~ ( in @ ( sK5_SY175 @ SV8 ) @ SV8 ) ) )
= $false )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(218,plain,
! [SV8: $i] :
( ( ( in @ ( setadjoin @ ( sK5_SY175 @ SV8 ) @ ( sK5_SY175 @ SV8 ) ) @ SV8 )
= $false )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(219,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(220,plain,
! [SV10: $i] :
( ( ~ ! [SY244: $i,SY245: $i] :
( ~ ~ ( ~ ( in @ SY244 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY245 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY244 )
| ( in @ SX4 @ SY245 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY245 )
| ( in @ SX4 @ SY244 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(221,plain,
! [SV10: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ! [SY263: $i] :
( ~ ( in @ SY263 @ SV39 )
| ( in @ SY263 @ SV10 ) )
| ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) ) )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(222,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( SV11 @ SV35 )
= $false )
| ( ( ~ ! [SY260: $i] :
( ~ ( SV11 @ SY260 )
| ( SV35 = SY260 ) ) )
= $true )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(223,plain,
! [SV12: $i,SV36: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY200 @ SV36 @ SV12 ) @ SV12 )
| ~ ~ ~ ! [SY270: $i] :
~ ~ ( ~ ( in @ SY270 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SY270 @ SV12 ) ) ) )
= $true )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(224,plain,
! [SV16: $i,SV29: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV29 ) )
= $true )
| ( ( in @ SV40 @ SV16 )
= $true )
| ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(225,plain,
! [SV29: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK7_SY237 @ SV16 @ SV29 ) @ SV29 ) )
= $false )
| ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(226,plain,
! [SV29: $i,SV16: $i] :
( ( ( in @ ( sK7_SY237 @ SV16 @ SV29 ) @ SV16 )
= $false )
| ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(227,plain,
! [SV37: $i,SV18: $i > $o] :
( ( ( SV18 @ SV37 )
= $false )
| ( ( ~ ! [SY261: $i] :
( ~ ( SV18 @ SY261 )
| ( SV37 = SY261 ) ) )
= $true )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(228,plain,
! [SV2: $i,SV19: $i] :
( ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(229,plain,
! [SV2: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
= $false )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(230,plain,
! [SV21: $i,SV4: $i > $i > $o] :
( ( ( ! [SY271: $i] :
~ ( ~ ( ~ ( in @ SY271 @ ( sK8_SY222 @ SV4 @ SV21 ) )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY271 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY271 ) )
| ( in @ SY271 @ ( sK8_SY222 @ SV4 @ SV21 ) ) ) ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(231,plain,
! [SV38: $i,SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
| ~ ! [SY262: $i] :
( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY262 )
| ( SV38 = SY262 ) ) )
= $true )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(232,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ ( sK9_SY226 @ SV5 @ SV22 ) )
| ~ ( in @ ( sK9_SY226 @ SV5 @ SV22 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(233,plain,
! [SV5: $i,SV41: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ SV41 )
| ~ ( in @ SV41 @ SV5 ) ) )
= $false )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(234,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY175 @ SV8 ) @ omega )
| ~ ( in @ ( sK5_SY175 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(235,plain,
! [SV8: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ omega )
| ( in @ SV42 @ SV8 ) )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( in @ ( setadjoin @ ( sK5_SY175 @ SV8 ) @ ( sK5_SY175 @ SV8 ) ) @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(236,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(237,plain,
! [SV10: $i] :
( ( ! [SY244: $i,SY245: $i] :
( ~ ~ ( ~ ( in @ SY244 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY245 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY244 )
| ( in @ SX4 @ SY245 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY245 )
| ( in @ SX4 @ SY244 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(238,plain,
! [SV10: $i,SV39: $i] :
( ( ( ~ ( ~ ! [SY263: $i] :
( ~ ( in @ SY263 @ SV39 )
| ( in @ SY263 @ SV10 ) )
| ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) ) )
= $false )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(239,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ! [SY260: $i] :
( ~ ( SV11 @ SY260 )
| ( SV35 = SY260 ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(240,plain,
! [SV12: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK6_SY200 @ SV36 @ SV12 ) @ SV12 )
| ~ ~ ~ ! [SY270: $i] :
~ ~ ( ~ ( in @ SY270 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SY270 @ SV12 ) ) )
= $false )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(241,plain,
! [SV16: $i,SV29: $i,SV40: $i] :
( ( ( in @ SV40 @ SV29 )
= $false )
| ( ( in @ SV40 @ SV16 )
= $true )
| ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(242,plain,
! [SV29: $i,SV16: $i] :
( ( ( in @ ( sK7_SY237 @ SV16 @ SV29 ) @ SV29 )
= $true )
| ( ( in @ SV29 @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(243,plain,
! [SV37: $i,SV18: $i > $o] :
( ( ( ! [SY261: $i] :
( ~ ( SV18 @ SY261 )
| ( SV37 = SY261 ) ) )
= $false )
| ( ( SV18 @ SV37 )
= $false )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(244,plain,
! [SV2: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
| ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(245,plain,
! [SV2: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 ) )
= $false )
| ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
= $false )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(246,plain,
! [SV2: $i,SV19: $i] :
( ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
= $false )
| ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
= $false )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(247,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
| ~ ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274 @ SV21 )
| ~ ( SV4 @ SY274 @ SV43 ) ) )
| ~ ( ~ ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV21 )
| ~ ( SV4 @ SY275 @ SV43 ) )
| ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) ) ) ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(248,plain,
! [SV38: $i,SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 ) )
= $true )
| ( ( ~ ! [SY262: $i] :
( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY262 )
| ( SV38 = SY262 ) ) )
= $true )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(249,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( sK9_SY226 @ SV5 @ SV22 ) )
| ~ ( in @ ( sK9_SY226 @ SV5 @ SV22 ) @ SV5 ) )
= $false )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(250,plain,
! [SV5: $i,SV41: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV41 )
| ~ ( in @ SV41 @ SV5 ) )
= $true )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(251,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK5_SY175 @ SV8 ) @ omega )
| ~ ( in @ ( sK5_SY175 @ SV8 ) @ SV8 ) )
= $false )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(252,plain,
! [SV8: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ omega ) )
= $true )
| ( ( in @ SV42 @ SV8 )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( in @ ( setadjoin @ ( sK5_SY175 @ SV8 ) @ ( sK5_SY175 @ SV8 ) ) @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(253,plain,
! [SV10: $i] :
( ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) )
| ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(254,plain,
! [SV10: $i,SV44: $i] :
( ( ! [SY276: $i] :
( ~ ~ ( ~ ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY276 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SY277: $i] :
( ~ ( in @ SY277 @ SV44 )
| ( in @ SY277 @ SY276 ) )
| ! [SY278: $i] :
( ~ ( in @ SY278 @ SY276 )
| ( in @ SY278 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(255,plain,
! [SV10: $i,SV39: $i] :
( ( ( ~ ! [SY263: $i] :
( ~ ( in @ SY263 @ SV39 )
| ( in @ SY263 @ SV10 ) )
| ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(256,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
| ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[239]) ).
thf(257,plain,
! [SV12: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK6_SY200 @ SV36 @ SV12 ) @ SV12 ) )
= $false )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(258,plain,
! [SV12: $i,SV36: $i] :
( ( ( ~ ~ ~ ! [SY270: $i] :
~ ~ ( ~ ( in @ SY270 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SY270 @ SV12 ) ) )
= $false )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(259,plain,
! [SV37: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ ( sK11_SY261 @ SV37 @ SV18 ) )
| ( SV37
= ( sK11_SY261 @ SV37 @ SV18 ) ) )
= $false )
| ( ( SV18 @ SV37 )
= $false )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[243]) ).
thf(260,plain,
! [SV2: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 ) )
= $false )
| ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(261,plain,
! [SV2: $i,SV19: $i] :
( ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
= $false )
| ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(262,plain,
! [SV2: $i,SV19: $i] :
( ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
= $true )
| ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
= $false )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(263,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
| ~ ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274 @ SV21 )
| ~ ( SV4 @ SY274 @ SV43 ) ) )
| ~ ( ~ ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV21 )
| ~ ( SV4 @ SY275 @ SV43 ) )
| ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(264,plain,
! [SV38: $i,SV21: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( ~ ! [SY262: $i] :
( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY262 )
| ( SV38 = SY262 ) ) )
= $true )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(265,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( sK9_SY226 @ SV5 @ SV22 ) ) )
= $false )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(266,plain,
! [SV22: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK9_SY226 @ SV5 @ SV22 ) @ SV5 ) )
= $false )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(267,plain,
! [SV5: $i,SV41: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV41 ) )
= $true )
| ( ( ~ ( in @ SV41 @ SV5 ) )
= $true )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(268,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK5_SY175 @ SV8 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(269,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK5_SY175 @ SV8 ) @ SV8 ) )
= $false )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(270,plain,
! [SV8: $i,SV42: $i] :
( ( ( in @ SV42 @ omega )
= $false )
| ( ( in @ SV42 @ SV8 )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( in @ ( setadjoin @ ( sK5_SY175 @ SV8 ) @ ( sK5_SY175 @ SV8 ) ) @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(271,plain,
! [SV10: $i] :
( ( ~ ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(272,plain,
! [SV10: $i] :
( ( ~ ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(273,plain,
! [SV45: $i,SV10: $i,SV44: $i] :
( ( ~ ~ ( ~ ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SV45 @ ( sK2_SY177 @ SV10 ) ) )
| ! [SY279: $i] :
( ~ ( in @ SY279 @ SV44 )
| ( in @ SY279 @ SV45 ) )
| ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(274,plain,
! [SV10: $i,SV39: $i] :
( ( ( ~ ! [SY263: $i] :
( ~ ( in @ SY263 @ SV39 )
| ( in @ SY263 @ SV10 ) ) )
= $true )
| ( ( ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(275,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(276,plain,
! [SV11: $i > $o,SV35: $i] :
( ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(277,plain,
! [SV12: $i,SV36: $i] :
( ( ( in @ ( sK6_SY200 @ SV36 @ SV12 ) @ SV12 )
= $true )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(278,plain,
! [SV12: $i,SV36: $i] :
( ( ( ~ ~ ! [SY270: $i] :
~ ~ ( ~ ( in @ SY270 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SY270 @ SV12 ) ) )
= $true )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(279,plain,
! [SV37: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ ( sK11_SY261 @ SV37 @ SV18 ) ) )
= $false )
| ( ( SV18 @ SV37 )
= $false )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(280,plain,
! [SV18: $i > $o,SV37: $i] :
( ( ( SV37
= ( sK11_SY261 @ SV37 @ SV18 ) )
= $false )
| ( ( SV18 @ SV37 )
= $false )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(281,plain,
! [SV2: $i,SV19: $i] :
( ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV19 )
= $true )
| ( ( in @ ( sK3_SY216 @ SV19 @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(282,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
| ~ ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274 @ SV21 )
| ~ ( SV4 @ SY274 @ SV43 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(283,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ( ~ ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV21 )
| ~ ( SV4 @ SY275 @ SV43 ) )
| ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(284,plain,
! [SV38: $i,SV21: $i,SV4: $i > $i > $o] :
( ( ( ! [SY262: $i] :
( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SY262 )
| ( SV38 = SY262 ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(285,plain,
! [SV5: $i,SV22: $i] :
( ( ( in @ SV22 @ ( sK9_SY226 @ SV5 @ SV22 ) )
= $true )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(286,plain,
! [SV22: $i,SV5: $i] :
( ( ( in @ ( sK9_SY226 @ SV5 @ SV22 ) @ SV5 )
= $true )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(287,plain,
! [SV5: $i,SV41: $i,SV22: $i] :
( ( ( in @ SV22 @ SV41 )
= $false )
| ( ( ~ ( in @ SV41 @ SV5 ) )
= $true )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(288,plain,
! [SV8: $i] :
( ( ( in @ ( sK5_SY175 @ SV8 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(289,plain,
! [SV8: $i] :
( ( ( in @ ( sK5_SY175 @ SV8 ) @ SV8 )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( in @ SY176 @ omega )
| ( in @ SY176 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(290,plain,
! [SV10: $i] :
( ( ! [SY239: $i] :
( ~ ( in @ SY239 @ ( sK2_SY177 @ SV10 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY239 )
| ( in @ SY179 @ SV10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(291,plain,
! [SV10: $i] :
( ( ! [SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( in @ SY241 @ SV10 )
| ~ ( in @ SY242 @ SV10 ) )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SY241 @ SY243 )
| ( in @ SY242 @ SY243 ) )
| ~ ( ~ ( in @ SY242 @ SY243 )
| ( in @ SY241 @ SY243 ) ) ) )
| ( SY241 = SY242 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(292,plain,
! [SV45: $i,SV10: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SV45 @ ( sK2_SY177 @ SV10 ) ) ) )
= $true )
| ( ( ! [SY279: $i] :
( ~ ( in @ SY279 @ SV44 )
| ( in @ SY279 @ SV45 ) )
| ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(293,plain,
! [SV10: $i,SV39: $i] :
( ( ( ! [SY263: $i] :
( ~ ( in @ SY263 @ SV39 )
| ( in @ SY263 @ SV10 ) ) )
= $false )
| ( ( ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(294,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(295,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(296,plain,
! [SV12: $i,SV36: $i] :
( ( ( ~ ! [SY270: $i] :
~ ~ ( ~ ( in @ SY270 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SY270 @ SV12 ) ) )
= $false )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(297,plain,
! [SV37: $i,SV18: $i > $o] :
( ( ( SV18 @ ( sK11_SY261 @ SV37 @ SV18 ) )
= $true )
| ( ( SV18 @ SV37 )
= $false )
| ( ( SV18
@ ( descr
@ ^ [SY215: $i] : ( SV18 @ SY215 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(298,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
| ~ ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274 @ SV21 )
| ~ ( SV4 @ SY274 @ SV43 ) ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(299,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV21 )
| ~ ( SV4 @ SY275 @ SV43 ) )
| ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(300,plain,
! [SV38: $i,SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
| ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[284]) ).
thf(301,plain,
! [SV22: $i,SV5: $i,SV41: $i] :
( ( ( in @ SV41 @ SV5 )
= $false )
| ( ( in @ SV22 @ SV41 )
= $false )
| ( ( in @ SV22 @ ( setunion @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(302,plain,
! [SV8: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ omega )
| ( in @ SV46 @ SV8 ) )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( in @ ( sK5_SY175 @ SV8 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(303,plain,
! [SV8: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ omega )
| ( in @ SV47 @ SV8 ) )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( in @ ( sK5_SY175 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(304,plain,
! [SV10: $i,SV48: $i] :
( ( ~ ( in @ SV48 @ ( sK2_SY177 @ SV10 ) )
| ! [SY281: $i] :
( ~ ( in @ SY281 @ SV48 )
| ( in @ SY281 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(305,plain,
! [SV10: $i,SV49: $i] :
( ( ! [SY282: $i] :
( ~ ~ ( ~ ( in @ SV49 @ SV10 )
| ~ ( in @ SY282 @ SV10 ) )
| ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY283 )
| ( in @ SY282 @ SY283 ) )
| ~ ( ~ ( in @ SY282 @ SY283 )
| ( in @ SV49 @ SY283 ) ) ) )
| ( SV49 = SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(306,plain,
! [SV45: $i,SV10: $i,SV44: $i] :
( ( ( ~ ( ~ ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SV45 @ ( sK2_SY177 @ SV10 ) ) ) )
= $false )
| ( ( ! [SY279: $i] :
( ~ ( in @ SY279 @ SV44 )
| ( in @ SY279 @ SV45 ) )
| ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(307,plain,
! [SV39: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
| ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 ) )
= $false )
| ( ( ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[293]) ).
thf(308,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ! [SY197: $i] :
~ ~ ( ~ ( SV11 @ SY197 )
| ~ ! [SY198: $i] :
( ~ ( SV11 @ SY198 )
| ( SY197 = SY198 ) ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(309,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ~ ( ~ ( SV11 @ ( sK14_SY197 @ SV35 @ SV11 ) )
| ~ ! [SY284: $i] :
( ~ ( SV11 @ SY284 )
| ( ( sK14_SY197 @ SV35 @ SV11 )
= SY284 ) ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[295]) ).
thf(310,plain,
! [SV12: $i,SV36: $i] :
( ( ( ! [SY270: $i] :
~ ~ ( ~ ( in @ SY270 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SY270 @ SV12 ) ) )
= $true )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(311,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) ) )
= $true )
| ( ( ~ ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274 @ SV21 )
| ~ ( SV4 @ SY274 @ SV43 ) ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(312,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV21 )
| ~ ( SV4 @ SY275 @ SV43 ) ) )
= $true )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(313,plain,
! [SV38: $i,SV21: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(314,plain,
! [SV4: $i > $i > $o,SV21: $i,SV38: $i] :
( ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(315,plain,
! [SV8: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ omega ) )
= $true )
| ( ( in @ SV46 @ SV8 )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( in @ ( sK5_SY175 @ SV8 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(316,plain,
! [SV8: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ omega ) )
= $true )
| ( ( in @ SV47 @ SV8 )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( in @ ( sK5_SY175 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(317,plain,
! [SV10: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( sK2_SY177 @ SV10 ) ) )
= $true )
| ( ( ! [SY281: $i] :
( ~ ( in @ SY281 @ SV48 )
| ( in @ SY281 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(318,plain,
! [SV50: $i,SV10: $i,SV49: $i] :
( ( ~ ~ ( ~ ( in @ SV49 @ SV10 )
| ~ ( in @ SV50 @ SV10 ) )
| ~ ! [SY285: $i] :
( ~ ( in @ SY285 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY285 )
| ( in @ SV50 @ SY285 ) )
| ~ ( ~ ( in @ SV50 @ SY285 )
| ( in @ SV49 @ SY285 ) ) ) )
| ( SV49 = SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(319,plain,
! [SV45: $i,SV10: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SV45 @ ( sK2_SY177 @ SV10 ) ) )
= $true )
| ( ( ! [SY279: $i] :
( ~ ( in @ SY279 @ SV44 )
| ( in @ SY279 @ SV45 ) )
| ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(320,plain,
! [SV39: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 ) )
= $false )
| ( ( ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(321,plain,
! [SV39: $i,SV10: $i] :
( ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(322,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ~ ( ~ ( SV11 @ ( sK15_SY197 @ SV35 @ SV11 ) )
| ~ ! [SY286: $i] :
( ~ ( SV11 @ SY286 )
| ( ( sK15_SY197 @ SV35 @ SV11 )
= SY286 ) ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[308]) ).
thf(323,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( ~ ( SV11 @ ( sK14_SY197 @ SV35 @ SV11 ) )
| ~ ! [SY284: $i] :
( ~ ( SV11 @ SY284 )
| ( ( sK14_SY197 @ SV35 @ SV11 )
= SY284 ) ) ) )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(324,plain,
! [SV12: $i,SV36: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( in @ SV51 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SV51 @ SV12 ) ) )
= $true )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(325,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $false )
| ( ( ~ ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274 @ SV21 )
| ~ ( SV4 @ SY274 @ SV43 ) ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(326,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV21 )
| ~ ( SV4 @ SY275 @ SV43 ) ) )
= $false )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(327,plain,
! [SV38: $i,SV21: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( ~ ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(328,plain,
! [SV38: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(329,plain,
! [SV8: $i,SV46: $i] :
( ( ( in @ SV46 @ omega )
= $false )
| ( ( in @ SV46 @ SV8 )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( in @ ( sK5_SY175 @ SV8 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(330,plain,
! [SV8: $i,SV47: $i] :
( ( ( in @ SV47 @ omega )
= $false )
| ( ( in @ SV47 @ SV8 )
= $true )
| ( ( in @ emptyset @ SV8 )
= $false )
| ( ( in @ ( sK5_SY175 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(331,plain,
! [SV10: $i,SV48: $i] :
( ( ( in @ SV48 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( ! [SY281: $i] :
( ~ ( in @ SY281 @ SV48 )
| ( in @ SY281 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(332,plain,
! [SV50: $i,SV10: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ SV49 @ SV10 )
| ~ ( in @ SV50 @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY285: $i] :
( ~ ( in @ SY285 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY285 )
| ( in @ SV50 @ SY285 ) )
| ~ ( ~ ( in @ SV50 @ SY285 )
| ( in @ SV49 @ SY285 ) ) ) )
| ( SV49 = SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(333,plain,
! [SV45: $i,SV10: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK2_SY177 @ SV10 ) ) )
= $true )
| ( ( ~ ( in @ SV45 @ ( sK2_SY177 @ SV10 ) ) )
= $true )
| ( ( ! [SY279: $i] :
( ~ ( in @ SY279 @ SV44 )
| ( in @ SY279 @ SV45 ) )
| ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(334,plain,
! [SV39: $i,SV10: $i] :
( ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( ~ ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(335,plain,
! [SV10: $i,SV39: $i] :
( ( ( ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(336,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( ~ ( SV11 @ ( sK15_SY197 @ SV35 @ SV11 ) )
| ~ ! [SY286: $i] :
( ~ ( SV11 @ SY286 )
| ( ( sK15_SY197 @ SV35 @ SV11 )
= SY286 ) ) ) )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(337,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ ( sK14_SY197 @ SV35 @ SV11 ) )
| ~ ! [SY284: $i] :
( ~ ( SV11 @ SY284 )
| ( ( sK14_SY197 @ SV35 @ SV11 )
= SY284 ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(338,plain,
! [SV12: $i,SV36: $i,SV51: $i] :
( ( ( ~ ( ~ ( in @ SV51 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SV51 @ SV12 ) ) )
= $false )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(339,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274 @ SV21 )
| ~ ( SV4 @ SY274 @ SV43 ) ) )
= $false )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(340,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV21 )
| ~ ( SV4 @ SY275 @ SV43 ) ) )
= $true )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(341,plain,
! [SV38: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY222: $i] :
~ ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SY222 )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY223 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY223 ) )
| ( in @ SY223 @ SY222 ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(342,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i] :
( ( ( ~ ! [SY287: $i] :
~ ( ~ ( ~ ( in @ SY287 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY287 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY287 ) )
| ( in @ SY287 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[328]) ).
thf(343,plain,
! [SV10: $i,SV48: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV48 )
| ( in @ SV52 @ SV10 ) )
= $true )
| ( ( in @ SV48 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(344,plain,
! [SV50: $i,SV10: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ SV10 )
| ~ ( in @ SV50 @ SV10 ) ) )
= $false )
| ( ( ~ ! [SY285: $i] :
( ~ ( in @ SY285 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY285 )
| ( in @ SV50 @ SY285 ) )
| ~ ( ~ ( in @ SV50 @ SY285 )
| ( in @ SV49 @ SY285 ) ) ) )
| ( SV49 = SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(345,plain,
! [SV45: $i,SV10: $i,SV44: $i] :
( ( ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( ~ ( in @ SV45 @ ( sK2_SY177 @ SV10 ) ) )
= $true )
| ( ( ! [SY279: $i] :
( ~ ( in @ SY279 @ SV44 )
| ( in @ SY279 @ SV45 ) )
| ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(346,plain,
! [SV10: $i,SV39: $i] :
( ( ( ~ ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(347,plain,
! [SV10: $i,SV39: $i] :
( ( ( ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(348,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ ( sK15_SY197 @ SV35 @ SV11 ) )
| ~ ! [SY286: $i] :
( ~ ( SV11 @ SY286 )
| ( ( sK15_SY197 @ SV35 @ SV11 )
= SY286 ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(349,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ ( sK14_SY197 @ SV35 @ SV11 ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(350,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ! [SY284: $i] :
( ~ ( SV11 @ SY284 )
| ( ( sK14_SY197 @ SV35 @ SV11 )
= SY284 ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(351,plain,
! [SV12: $i,SV36: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( sK6_SY200 @ SV36 @ SV12 ) )
| ~ ( in @ SV51 @ SV12 ) )
= $true )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(352,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV21 )
| ~ ( SV4 @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV43 ) ) )
= $false )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[339]) ).
thf(353,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( in @ SV53 @ SV21 )
| ~ ( SV4 @ SV53 @ SV43 ) ) )
= $true )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(354,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i] :
( ( ( ~ ! [SY290: $i] :
~ ( ~ ( ~ ( in @ SY290 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY290 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY290 ) )
| ( in @ SY290 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[341]) ).
thf(355,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i] :
( ( ( ! [SY287: $i] :
~ ( ~ ( ~ ( in @ SY287 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY287 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY287 ) )
| ( in @ SY287 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) ) ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(356,plain,
! [SV10: $i,SV48: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV48 ) )
= $true )
| ( ( in @ SV52 @ SV10 )
= $true )
| ( ( in @ SV48 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(357,plain,
! [SV50: $i,SV10: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV10 )
| ~ ( in @ SV50 @ SV10 ) )
= $true )
| ( ( ~ ! [SY285: $i] :
( ~ ( in @ SY285 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY285 )
| ( in @ SV50 @ SY285 ) )
| ~ ( ~ ( in @ SV50 @ SY285 )
| ( in @ SV49 @ SY285 ) ) ) )
| ( SV49 = SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(358,plain,
! [SV44: $i,SV10: $i,SV45: $i] :
( ( ( in @ SV45 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( ! [SY279: $i] :
( ~ ( in @ SY279 @ SV44 )
| ( in @ SY279 @ SV45 ) )
| ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(359,plain,
! [SV10: $i,SV39: $i] :
( ( ( ! [SY264: $i] :
~ ( in @ SY264 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(360,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(361,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ ( sK15_SY197 @ SV35 @ SV11 ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(362,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ~ ! [SY286: $i] :
( ~ ( SV11 @ SY286 )
| ( ( sK15_SY197 @ SV35 @ SV11 )
= SY286 ) ) )
= $false )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(363,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( SV11 @ ( sK14_SY197 @ SV35 @ SV11 ) )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(364,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ! [SY284: $i] :
( ~ ( SV11 @ SY284 )
| ( ( sK14_SY197 @ SV35 @ SV11 )
= SY284 ) ) )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(365,plain,
! [SV12: $i,SV36: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( sK6_SY200 @ SV36 @ SV12 ) ) )
= $true )
| ( ( ~ ( in @ SV51 @ SV12 ) )
= $true )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(366,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV21 )
| ~ ( SV4 @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV43 ) ) )
= $true )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(367,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( ~ ( ~ ( in @ SV53 @ SV21 )
| ~ ( SV4 @ SV53 @ SV43 ) ) )
= $false )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(368,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i] :
( ( ( ! [SY290: $i] :
~ ( ~ ( ~ ( in @ SY290 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY224: $i] :
~ ~ ( ~ ( in @ SY224 @ SV21 )
| ~ ( SV4 @ SY224 @ SY290 ) ) )
| ~ ( ~ ~ ! [SY225: $i] :
~ ~ ( ~ ( in @ SY225 @ SV21 )
| ~ ( SV4 @ SY225 @ SY290 ) )
| ( in @ SY290 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) ) ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(369,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV55: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY293: $i] :
~ ~ ( ~ ( in @ SY293 @ SV21 )
| ~ ( SV4 @ SY293 @ SV55 ) ) )
| ~ ( ~ ~ ! [SY294: $i] :
~ ~ ( ~ ( in @ SY294 @ SV21 )
| ~ ( SV4 @ SY294 @ SV55 ) )
| ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) ) ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(370,plain,
! [SV10: $i,SV48: $i,SV52: $i] :
( ( ( in @ SV52 @ SV48 )
= $false )
| ( ( in @ SV52 @ SV10 )
= $true )
| ( ( in @ SV48 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(371,plain,
! [SV50: $i,SV10: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV10 ) )
= $true )
| ( ( ~ ( in @ SV50 @ SV10 ) )
= $true )
| ( ( ~ ! [SY285: $i] :
( ~ ( in @ SY285 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY285 )
| ( in @ SV50 @ SY285 ) )
| ~ ( ~ ( in @ SV50 @ SY285 )
| ( in @ SV49 @ SY285 ) ) ) )
| ( SV49 = SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(372,plain,
! [SV10: $i,SV45: $i,SV44: $i] :
( ( ( ! [SY279: $i] :
( ~ ( in @ SY279 @ SV44 )
| ( in @ SY279 @ SV45 ) ) )
= $true )
| ( ( ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true )
| ( ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ SV45 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(373,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(374,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( in @ SV54 @ SV39 )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(375,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( SV11 @ ( sK15_SY197 @ SV35 @ SV11 ) )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(376,plain,
! [SV35: $i,SV11: $i > $o] :
( ( ( ! [SY286: $i] :
( ~ ( SV11 @ SY286 )
| ( ( sK15_SY197 @ SV35 @ SV11 )
= SY286 ) ) )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(377,plain,
! [SV35: $i,SV57: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ SV57 )
| ( ( sK14_SY197 @ SV35 @ SV11 )
= SV57 ) )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(378,plain,
! [SV12: $i,SV36: $i,SV51: $i] :
( ( ( in @ SV51 @ ( sK6_SY200 @ SV36 @ SV12 ) )
= $false )
| ( ( ~ ( in @ SV51 @ SV12 ) )
= $true )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(379,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( ~ ( in @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV21 )
| ~ ( SV4 @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV43 ) )
= $false )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(380,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV21 )
| ~ ( SV4 @ SV53 @ SV43 ) )
= $true )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(381,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV58: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY295: $i] :
~ ~ ( ~ ( in @ SY295 @ SV21 )
| ~ ( SV4 @ SY295 @ SV58 ) ) )
| ~ ( ~ ~ ! [SY296: $i] :
~ ~ ( ~ ( in @ SY296 @ SV21 )
| ~ ( SV4 @ SY296 @ SV58 ) )
| ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) ) ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(382,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY293: $i] :
~ ~ ( ~ ( in @ SY293 @ SV21 )
| ~ ( SV4 @ SY293 @ SV55 ) ) )
| ~ ( ~ ~ ! [SY294: $i] :
~ ~ ( ~ ( in @ SY294 @ SV21 )
| ~ ( SV4 @ SY294 @ SV55 ) )
| ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(383,plain,
! [SV50: $i,SV10: $i,SV49: $i] :
( ( ( in @ SV49 @ SV10 )
= $false )
| ( ( ~ ( in @ SV50 @ SV10 ) )
= $true )
| ( ( ~ ! [SY285: $i] :
( ~ ( in @ SY285 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY285 )
| ( in @ SV50 @ SY285 ) )
| ~ ( ~ ( in @ SV50 @ SY285 )
| ( in @ SV49 @ SY285 ) ) ) )
| ( SV49 = SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(384,plain,
! [SV10: $i,SV45: $i,SV44: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV44 )
| ( in @ SV59 @ SV45 ) )
= $true )
| ( ( ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true )
| ( ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ SV45 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(385,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( in @ SV56 @ SV39 )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(386,plain,
! [SV54: $i,SV39: $i,SV10: $i] :
( ( ( ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(387,plain,
! [SV35: $i,SV60: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ SV60 )
| ( ( sK15_SY197 @ SV35 @ SV11 )
= SV60 ) )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(388,plain,
! [SV35: $i,SV57: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ SV57 ) )
= $true )
| ( ( ( sK14_SY197 @ SV35 @ SV11 )
= SV57 )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(389,plain,
! [SV36: $i,SV12: $i,SV51: $i] :
( ( ( in @ SV51 @ SV12 )
= $false )
| ( ( in @ SV51 @ ( sK6_SY200 @ SV36 @ SV12 ) )
= $false )
| ( ( in @ SV36 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(390,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( ~ ( in @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV21 ) )
= $false )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(391,plain,
! [SV21: $i,SV43: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV43 ) )
= $false )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(392,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV21 ) )
= $true )
| ( ( ~ ( SV4 @ SV53 @ SV43 ) )
= $true )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(393,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV58: $i] :
( ( ( ~ ( ~ ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY295: $i] :
~ ~ ( ~ ( in @ SY295 @ SV21 )
| ~ ( SV4 @ SY295 @ SV58 ) ) )
| ~ ( ~ ~ ! [SY296: $i] :
~ ~ ( ~ ( in @ SY296 @ SV21 )
| ~ ( SV4 @ SY296 @ SV58 ) )
| ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(394,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY293: $i] :
~ ~ ( ~ ( in @ SY293 @ SV21 )
| ~ ( SV4 @ SY293 @ SV55 ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(395,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ( ~ ~ ! [SY294: $i] :
~ ~ ( ~ ( in @ SY294 @ SV21 )
| ~ ( SV4 @ SY294 @ SV55 ) )
| ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(396,plain,
! [SV49: $i,SV10: $i,SV50: $i] :
( ( ( in @ SV50 @ SV10 )
= $false )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( ~ ! [SY285: $i] :
( ~ ( in @ SY285 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY285 )
| ( in @ SV50 @ SY285 ) )
| ~ ( ~ ( in @ SV50 @ SY285 )
| ( in @ SV49 @ SY285 ) ) ) )
| ( SV49 = SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(397,plain,
! [SV10: $i,SV45: $i,SV44: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV44 ) )
= $true )
| ( ( in @ SV59 @ SV45 )
= $true )
| ( ( ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true )
| ( ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ SV45 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(398,plain,
! [SV56: $i,SV39: $i,SV10: $i] :
( ( ( ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY265 @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY266 @ SV39 ) )
| ~ ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SY265 )
| ~ ( in @ SY267 @ SV39 ) ) )
| ~ ! [SY254: $i] :
( ~ ( in @ SY254 @ ( sK2_SY177 @ SV10 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY254 )
| ( in @ SX6 @ SY265 ) )
| ( in @ SY266 @ SY254 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(399,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ~ ! [SY297: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY297 @ SV39 ) )
| ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
| ~ ! [SY299: $i] :
( ~ ( in @ SY299 @ ( sK2_SY177 @ SV10 ) )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SY299 )
| ( in @ SY300 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ SY297 @ SY299 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[386]) ).
thf(400,plain,
! [SV35: $i,SV60: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ SV60 ) )
= $true )
| ( ( ( sK15_SY197 @ SV35 @ SV11 )
= SV60 )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(401,plain,
! [SV35: $i,SV57: $i,SV11: $i > $o] :
( ( ( SV11 @ SV57 )
= $false )
| ( ( ( sK14_SY197 @ SV35 @ SV11 )
= SV57 )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV35
= ( sK10_SY260 @ SV35 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(402,plain,
! [SV21: $i,SV4: $i > $i > $o,SV43: $i] :
( ( ( in @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV21 )
= $true )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(403,plain,
! [SV21: $i,SV43: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK17_SY274 @ SV43 @ SV4 @ SV21 ) @ SV43 )
= $true )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(404,plain,
! [SV43: $i,SV4: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( in @ SV53 @ SV21 )
= $false )
| ( ( ~ ( SV4 @ SV53 @ SV43 ) )
= $true )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(405,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV58: $i] :
( ( ( ~ ( ~ ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY295: $i] :
~ ~ ( ~ ( in @ SY295 @ SV21 )
| ~ ( SV4 @ SY295 @ SV58 ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(406,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ( ~ ~ ! [SY296: $i] :
~ ~ ( ~ ( in @ SY296 @ SV21 )
| ~ ( SV4 @ SY296 @ SV58 ) )
| ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) ) ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(407,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY293: $i] :
~ ~ ( ~ ( in @ SY293 @ SV21 )
| ~ ( SV4 @ SY293 @ SV55 ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(408,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY294: $i] :
~ ~ ( ~ ( in @ SY294 @ SV21 )
| ~ ( SV4 @ SY294 @ SV55 ) )
| ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(409,plain,
! [SV50: $i,SV49: $i,SV10: $i] :
( ( ( ~ ! [SY285: $i] :
( ~ ( in @ SY285 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY285 )
| ( in @ SV50 @ SY285 ) )
| ~ ( ~ ( in @ SV50 @ SY285 )
| ( in @ SV49 @ SY285 ) ) ) ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(410,plain,
! [SV10: $i,SV45: $i,SV44: $i,SV59: $i] :
( ( ( in @ SV59 @ SV44 )
= $false )
| ( ( in @ SV59 @ SV45 )
= $true )
| ( ( ! [SY280: $i] :
( ~ ( in @ SY280 @ SV45 )
| ( in @ SY280 @ SV44 ) ) )
= $true )
| ( ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ SV45 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(411,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ~ ! [SY301: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY301 @ SV39 ) )
| ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
| ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK2_SY177 @ SV10 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ SY301 @ SY303 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[398]) ).
thf(412,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ! [SY297: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY297 @ SV39 ) )
| ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
| ~ ! [SY299: $i] :
( ~ ( in @ SY299 @ ( sK2_SY177 @ SV10 ) )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SY299 )
| ( in @ SY300 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ SY297 @ SY299 ) ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(413,plain,
! [SV35: $i,SV60: $i,SV11: $i > $o] :
( ( ( SV11 @ SV60 )
= $false )
| ( ( ( sK15_SY197 @ SV35 @ SV11 )
= SV60 )
= $true )
| ( ( SV11 @ SV35 )
= $false )
| ( ( SV11 @ ( sK10_SY260 @ SV35 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(414,plain,
! [SV21: $i,SV43: $i,SV53: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ SV53 @ SV43 )
= $false )
| ( ( in @ SV53 @ SV21 )
= $false )
| ( ( in @ SV43 @ ( sK8_SY222 @ SV4 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(415,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
| ~ ! [SY295: $i] :
~ ~ ( ~ ( in @ SY295 @ SV21 )
| ~ ( SV4 @ SY295 @ SV58 ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(416,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY296: $i] :
~ ~ ( ~ ( in @ SY296 @ SV21 )
| ~ ( SV4 @ SY296 @ SV58 ) )
| ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(417,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) ) )
= $true )
| ( ( ~ ! [SY293: $i] :
~ ~ ( ~ ( in @ SY293 @ SV21 )
| ~ ( SV4 @ SY293 @ SV55 ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(418,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY294: $i] :
~ ~ ( ~ ( in @ SY294 @ SV21 )
| ~ ( SV4 @ SY294 @ SV55 ) ) )
= $true )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(419,plain,
! [SV50: $i,SV49: $i,SV10: $i] :
( ( ( ! [SY285: $i] :
( ~ ( in @ SY285 @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ SY285 )
| ( in @ SV50 @ SY285 ) )
| ~ ( ~ ( in @ SV50 @ SY285 )
| ( in @ SV49 @ SY285 ) ) ) ) )
= $false )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(420,plain,
! [SV10: $i,SV59: $i,SV44: $i,SV45: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV45 )
| ( in @ SV61 @ SV44 ) )
= $true )
| ( ( in @ SV59 @ SV45 )
= $true )
| ( ( in @ SV59 @ SV44 )
= $false )
| ( ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ SV45 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(421,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ! [SY301: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY301 @ SV39 ) )
| ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
| ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK2_SY177 @ SV10 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ SY301 @ SY303 ) ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(422,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ! [SY297: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY297 @ SV39 ) )
| ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
| ~ ! [SY299: $i] :
( ~ ( in @ SY299 @ ( sK2_SY177 @ SV10 ) )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SY299 )
| ( in @ SY300 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ SY297 @ SY299 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(423,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) ) )
= $true )
| ( ( ~ ! [SY295: $i] :
~ ~ ( ~ ( in @ SY295 @ SV21 )
| ~ ( SV4 @ SY295 @ SV58 ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(424,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY296: $i] :
~ ~ ( ~ ( in @ SY296 @ SV21 )
| ~ ( SV4 @ SY296 @ SV58 ) ) )
= $true )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(425,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV55: $i] :
( ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( ~ ! [SY293: $i] :
~ ~ ( ~ ( in @ SY293 @ SV21 )
| ~ ( SV4 @ SY293 @ SV55 ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(426,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ! [SY294: $i] :
~ ~ ( ~ ( in @ SY294 @ SV21 )
| ~ ( SV4 @ SY294 @ SV55 ) ) )
= $false )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(427,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( ~ ( in @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( ~ ( ~ ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) )
| ~ ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) ) ) )
= $false )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[419]) ).
thf(428,plain,
! [SV10: $i,SV59: $i,SV44: $i,SV45: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV45 ) )
= $true )
| ( ( in @ SV61 @ SV44 )
= $true )
| ( ( in @ SV59 @ SV45 )
= $true )
| ( ( in @ SV59 @ SV44 )
= $false )
| ( ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ SV45 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(429,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ! [SY301: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ SY301 @ SV39 ) )
| ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
| ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ ( sK2_SY177 @ SV10 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ SY301 @ SY303 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(430,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) )
| ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
| ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ ( sK2_SY177 @ SV10 ) )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SY306 )
| ( in @ SY300 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SY306 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[422]) ).
thf(431,plain,
! [SV21: $i,SV4: $i > $i > $o,SV38: $i,SV58: $i] :
( ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( ~ ! [SY295: $i] :
~ ~ ( ~ ( in @ SY295 @ SV21 )
| ~ ( SV4 @ SY295 @ SV58 ) ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(432,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ~ ! [SY296: $i] :
~ ~ ( ~ ( in @ SY296 @ SV21 )
| ~ ( SV4 @ SY296 @ SV58 ) ) )
= $false )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(433,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY293: $i] :
~ ~ ( ~ ( in @ SY293 @ SV21 )
| ~ ( SV4 @ SY293 @ SV55 ) ) )
= $false )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(434,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY294: $i] :
~ ~ ( ~ ( in @ SY294 @ SV21 )
| ~ ( SV4 @ SY294 @ SV55 ) ) )
= $true )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(435,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( ~ ( in @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) @ ( sK2_SY177 @ SV10 ) ) )
= $false )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(436,plain,
! [SV10: $i,SV50: $i,SV49: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) )
| ~ ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) ) ) )
= $false )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(437,plain,
! [SV10: $i,SV59: $i,SV44: $i,SV45: $i,SV61: $i] :
( ( ( in @ SV61 @ SV45 )
= $false )
| ( ( in @ SV61 @ SV44 )
= $true )
| ( ( in @ SV59 @ SV45 )
= $true )
| ( ( in @ SV59 @ SV44 )
= $false )
| ( ( in @ SV44 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ SV45 @ ( sK2_SY177 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(438,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) )
| ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
| ~ ! [SY309: $i] :
( ~ ( in @ SY309 @ ( sK2_SY177 @ SV10 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY309 )
| ( in @ SY304 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SY309 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[429]) ).
thf(439,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) )
| ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
| ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ ( sK2_SY177 @ SV10 ) )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SY306 )
| ( in @ SY300 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SY306 ) ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(440,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY295: $i] :
~ ~ ( ~ ( in @ SY295 @ SV21 )
| ~ ( SV4 @ SY295 @ SV58 ) ) )
= $false )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(441,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i] :
( ( ( ! [SY296: $i] :
~ ~ ( ~ ( in @ SY296 @ SV21 )
| ~ ( SV4 @ SY296 @ SV58 ) ) )
= $true )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(442,plain,
! [SV21: $i,SV4: $i > $i > $o,SV55: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV21 )
| ~ ( SV4 @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV55 ) ) )
= $false )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[433]) ).
thf(443,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( in @ SV62 @ SV21 )
| ~ ( SV4 @ SV62 @ SV55 ) ) )
= $true )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(444,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( in @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(445,plain,
! [SV10: $i,SV50: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) )
| ~ ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(446,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) )
| ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
| ~ ! [SY309: $i] :
( ~ ( in @ SY309 @ ( sK2_SY177 @ SV10 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY309 )
| ( in @ SY304 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SY309 ) ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(447,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) )
| ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
| ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ ( sK2_SY177 @ SV10 ) )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SY306 )
| ( in @ SY300 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SY306 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(448,plain,
! [SV21: $i,SV4: $i > $i > $o,SV58: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV21 )
| ~ ( SV4 @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV58 ) ) )
= $false )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[440]) ).
thf(449,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( in @ SV63 @ SV21 )
| ~ ( SV4 @ SV63 @ SV58 ) ) )
= $true )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(450,plain,
! [SV21: $i,SV4: $i > $i > $o,SV55: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV21 )
| ~ ( SV4 @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV55 ) ) )
= $true )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(451,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i,SV62: $i] :
( ( ( ~ ( ~ ( in @ SV62 @ SV21 )
| ~ ( SV4 @ SV62 @ SV55 ) ) )
= $false )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(452,plain,
! [SV10: $i,SV50: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(453,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) )
| ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
| ~ ! [SY309: $i] :
( ~ ( in @ SY309 @ ( sK2_SY177 @ SV10 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY309 )
| ( in @ SY304 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SY309 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(454,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) )
| ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(455,plain,
! [SV39: $i,SV54: $i,SV10: $i] :
( ( ( ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ ( sK2_SY177 @ SV10 ) )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SY306 )
| ( in @ SY300 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SY306 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(456,plain,
! [SV21: $i,SV4: $i > $i > $o,SV58: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV21 )
| ~ ( SV4 @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV58 ) ) )
= $true )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(457,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i,SV63: $i] :
( ( ( ~ ( ~ ( in @ SV63 @ SV21 )
| ~ ( SV4 @ SV63 @ SV58 ) ) )
= $false )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(458,plain,
! [SV21: $i,SV4: $i > $i > $o,SV55: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV21 )
| ~ ( SV4 @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV55 ) )
= $false )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(459,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ SV21 )
| ~ ( SV4 @ SV62 @ SV55 ) )
= $true )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(460,plain,
! [SV10: $i,SV50: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(461,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) )
| ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(462,plain,
! [SV39: $i,SV56: $i,SV10: $i] :
( ( ( ~ ! [SY309: $i] :
( ~ ( in @ SY309 @ ( sK2_SY177 @ SV10 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY309 )
| ( in @ SY304 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SY309 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(463,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) )
| ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(464,plain,
! [SV39: $i,SV54: $i,SV10: $i] :
( ( ( ! [SY306: $i] :
( ~ ( in @ SY306 @ ( sK2_SY177 @ SV10 ) )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SY306 )
| ( in @ SY300 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SY306 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(465,plain,
! [SV21: $i,SV4: $i > $i > $o,SV58: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV21 )
| ~ ( SV4 @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV58 ) )
= $false )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(466,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV21 )
| ~ ( SV4 @ SV63 @ SV58 ) )
= $true )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(467,plain,
! [SV21: $i,SV4: $i > $i > $o,SV55: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV21 ) )
= $false )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(468,plain,
! [SV21: $i,SV55: $i,SV38: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV55 ) )
= $false )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(469,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ SV21 ) )
= $true )
| ( ( ~ ( SV4 @ SV62 @ SV55 ) )
= $true )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(470,plain,
! [SV10: $i,SV50: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(471,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(472,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) )
| ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(473,plain,
! [SV39: $i,SV56: $i,SV10: $i] :
( ( ( ! [SY309: $i] :
( ~ ( in @ SY309 @ ( sK2_SY177 @ SV10 ) )
| ! [SY304: $i] :
( ~ ( in @ SY304 @ SY309 )
| ( in @ SY304 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SY309 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(474,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) )
| ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(475,plain,
! [SV39: $i,SV54: $i,SV10: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ ( sK2_SY177 @ SV10 ) )
| ! [SY311: $i] :
( ~ ( in @ SY311 @ SV64 )
| ( in @ SY311 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV64 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(476,plain,
! [SV21: $i,SV4: $i > $i > $o,SV58: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV21 ) )
= $false )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(477,plain,
! [SV21: $i,SV58: $i,SV38: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV58 ) )
= $false )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(478,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV21 ) )
= $true )
| ( ( ~ ( SV4 @ SV63 @ SV58 ) )
= $true )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(479,plain,
! [SV21: $i,SV4: $i > $i > $o,SV55: $i,SV38: $i] :
( ( ( in @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV21 )
= $true )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(480,plain,
! [SV21: $i,SV55: $i,SV38: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK24_SY293 @ SV38 @ SV55 @ SV4 @ SV21 ) @ SV55 )
= $true )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(481,plain,
! [SV38: $i,SV55: $i,SV4: $i > $i > $o,SV21: $i,SV62: $i] :
( ( ( in @ SV62 @ SV21 )
= $false )
| ( ( ~ ( SV4 @ SV62 @ SV55 ) )
= $true )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(482,plain,
! [SV10: $i,SV50: $i,SV49: $i] :
( ( ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(483,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) )
= $false )
| ( ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $false )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(484,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) )
| ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(485,plain,
! [SV39: $i,SV56: $i,SV10: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ ( sK2_SY177 @ SV10 ) )
| ! [SY312: $i] :
( ~ ( in @ SY312 @ SV65 )
| ( in @ SY312 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV65 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(486,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(487,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(488,plain,
! [SV39: $i,SV54: $i,SV10: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ ( sK2_SY177 @ SV10 ) ) )
= $true )
| ( ( ! [SY311: $i] :
( ~ ( in @ SY311 @ SV64 )
| ( in @ SY311 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV64 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(489,plain,
! [SV21: $i,SV4: $i > $i > $o,SV58: $i,SV38: $i] :
( ( ( in @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV21 )
= $true )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(490,plain,
! [SV21: $i,SV58: $i,SV38: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK25_SY295 @ SV38 @ SV58 @ SV4 @ SV21 ) @ SV58 )
= $true )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(491,plain,
! [SV38: $i,SV58: $i,SV4: $i > $i > $o,SV21: $i,SV63: $i] :
( ( ( in @ SV63 @ SV21 )
= $false )
| ( ( ~ ( SV4 @ SV63 @ SV58 ) )
= $true )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(492,plain,
! [SV38: $i,SV21: $i,SV55: $i,SV62: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ SV62 @ SV55 )
= $false )
| ( ( in @ SV62 @ SV21 )
= $false )
| ( ( in @ SV55 @ ( sK16_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV38
= ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(493,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
| ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) )
= $false )
| ( ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(494,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) )
= $false )
| ( ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $false )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(495,plain,
! [SV10: $i,SV50: $i,SV49: $i] :
( ( ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $false )
| ( ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $false )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(496,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(497,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(498,plain,
! [SV39: $i,SV56: $i,SV10: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ ( sK2_SY177 @ SV10 ) ) )
= $true )
| ( ( ! [SY312: $i] :
( ~ ( in @ SY312 @ SV65 )
| ( in @ SY312 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV65 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(499,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(500,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(501,plain,
! [SV39: $i,SV54: $i,SV10: $i,SV64: $i] :
( ( ( in @ SV64 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( ! [SY311: $i] :
( ~ ( in @ SY311 @ SV64 )
| ( in @ SY311 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
| ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV64 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(502,plain,
! [SV38: $i,SV21: $i,SV58: $i,SV63: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ SV63 @ SV58 )
= $false )
| ( ( in @ SV63 @ SV21 )
= $false )
| ( ( in @ SV58 @ ( sK18_SY222 @ SV38 @ SV4 @ SV21 ) )
= $true )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ SV38 )
= $false )
| ( ( SV4 @ ( sK4_SY219 @ SV4 @ SV21 ) @ ( sK12_SY262 @ SV38 @ SV21 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(503,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) ) )
= $false )
| ( ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(504,plain,
! [SV10: $i,SV50: $i,SV49: $i] :
( ( ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $false )
| ( ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(505,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $true )
| ( ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $false )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(506,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(507,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(508,plain,
! [SV39: $i,SV56: $i,SV10: $i,SV65: $i] :
( ( ( in @ SV65 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( ! [SY312: $i] :
( ~ ( in @ SY312 @ SV65 )
| ( in @ SY312 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
| ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV65 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(509,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(510,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(511,plain,
! [SV10: $i,SV39: $i,SV54: $i,SV64: $i] :
( ( ( ! [SY311: $i] :
( ~ ( in @ SY311 @ SV64 )
| ( in @ SY311 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) ) )
= $true )
| ( ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV64 )
= $true )
| ( ( in @ SV64 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(512,plain,
! [SV10: $i,SV49: $i,SV50: $i] :
( ( ( in @ SV50 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $true )
| ( ( in @ SV49 @ ( sK21_SY285 @ SV50 @ SV49 @ SV10 ) )
= $true )
| ( ( SV49 = SV50 )
= $true )
| ( ( in @ SV49 @ SV10 )
= $false )
| ( ( in @ SV50 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(513,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
| ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(514,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(515,plain,
! [SV10: $i,SV39: $i,SV56: $i,SV65: $i] :
( ( ( ! [SY312: $i] :
( ~ ( in @ SY312 @ SV65 )
| ( in @ SY312 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) ) )
= $true )
| ( ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV65 )
= $true )
| ( ( in @ SV65 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(516,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ~ ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(517,plain,
! [SV54: $i,SV39: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(518,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( ! [SY298: $i] :
~ ~ ( ~ ( in @ SY298 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SY298 @ SV39 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(519,plain,
! [SV10: $i,SV39: $i,SV54: $i,SV64: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ SV64 )
| ( in @ SV66 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
= $true )
| ( ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV64 )
= $true )
| ( ( in @ SV64 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(520,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ~ ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(521,plain,
! [SV56: $i,SV39: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(522,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( ! [SY302: $i] :
~ ~ ( ~ ( in @ SY302 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SY302 @ SV39 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(523,plain,
! [SV10: $i,SV39: $i,SV56: $i,SV65: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV65 )
| ( in @ SV67 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
= $true )
| ( ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV65 )
= $true )
| ( ( in @ SV65 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(524,plain,
! [SV10: $i,SV39: $i,SV54: $i] :
( ( ( in @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(525,plain,
! [SV54: $i,SV39: $i,SV10: $i] :
( ( ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV39 )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(526,plain,
! [SV10: $i,SV39: $i,SV54: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ( in @ SV68 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SV68 @ SV39 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(527,plain,
! [SV10: $i,SV39: $i,SV54: $i,SV64: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ SV64 ) )
= $true )
| ( ( in @ SV66 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
= $true )
| ( ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV64 )
= $true )
| ( ( in @ SV64 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(528,plain,
! [SV10: $i,SV39: $i,SV56: $i] :
( ( ( in @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) @ ( sK2_SY177 @ SV10 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(529,plain,
! [SV56: $i,SV39: $i,SV10: $i] :
( ( ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV39 )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(530,plain,
! [SV10: $i,SV39: $i,SV56: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ( in @ SV69 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SV69 @ SV39 ) ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(531,plain,
! [SV10: $i,SV39: $i,SV56: $i,SV65: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV65 ) )
= $true )
| ( ( in @ SV67 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
= $true )
| ( ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV65 )
= $true )
| ( ( in @ SV65 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(532,plain,
! [SV10: $i,SV39: $i,SV54: $i,SV68: $i] :
( ( ( ~ ( ~ ( in @ SV68 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SV68 @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(533,plain,
! [SV10: $i,SV39: $i,SV54: $i,SV64: $i,SV66: $i] :
( ( ( in @ SV66 @ SV64 )
= $false )
| ( ( in @ SV66 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
= $true )
| ( ( in @ ( sK22_SY297 @ SV10 @ SV39 @ SV54 ) @ SV64 )
= $true )
| ( ( in @ SV64 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(534,plain,
! [SV10: $i,SV39: $i,SV56: $i,SV69: $i] :
( ( ( ~ ( ~ ( in @ SV69 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SV69 @ SV39 ) ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(535,plain,
! [SV10: $i,SV39: $i,SV56: $i,SV65: $i,SV67: $i] :
( ( ( in @ SV67 @ SV65 )
= $false )
| ( ( in @ SV67 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
= $true )
| ( ( in @ ( sK23_SY301 @ SV10 @ SV39 @ SV56 ) @ SV65 )
= $true )
| ( ( in @ SV65 @ ( sK2_SY177 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(536,plain,
! [SV10: $i,SV39: $i,SV54: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
| ~ ( in @ SV68 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(537,plain,
! [SV10: $i,SV39: $i,SV56: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
| ~ ( in @ SV69 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(538,plain,
! [SV10: $i,SV39: $i,SV54: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) ) )
= $true )
| ( ( ~ ( in @ SV68 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(539,plain,
! [SV10: $i,SV39: $i,SV56: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) ) )
= $true )
| ( ( ~ ( in @ SV69 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(540,plain,
! [SV10: $i,SV39: $i,SV54: $i,SV68: $i] :
( ( ( in @ SV68 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
= $false )
| ( ( ~ ( in @ SV68 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(541,plain,
! [SV10: $i,SV39: $i,SV56: $i,SV69: $i] :
( ( ( in @ SV69 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
= $false )
| ( ( ~ ( in @ SV69 @ SV39 ) )
= $true )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(542,plain,
! [SV10: $i,SV54: $i,SV39: $i,SV68: $i] :
( ( ( in @ SV68 @ SV39 )
= $false )
| ( ( in @ SV68 @ ( sK19_SY265 @ SV54 @ SV39 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV10 )
= $false )
| ( ( in @ SV54 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(543,plain,
! [SV10: $i,SV56: $i,SV39: $i,SV69: $i] :
( ( ( in @ SV69 @ SV39 )
= $false )
| ( ( in @ SV69 @ ( sK20_SY265 @ SV56 @ SV39 @ SV10 ) )
= $false )
| ( ( in @ ( sK13_SY263 @ SV10 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV56 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(544,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,543,542,535,533,529,528,525,524,512,505,504,502,495,492,490,489,480,479,444,437,414,413,403,402,401,389,375,370,363,330,329,301,297,286,285,281,280,277,270,262,261,246,242,241,226,216,215,214,189,157,146,140,139,138,131,130,129,122,112,104,83]) ).
thf(545,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU503^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:26:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.05/0.39
% 1.05/0.39 No.of.Axioms: 0
% 1.05/0.39
% 1.05/0.39 Length.of.Defs: 4686
% 1.05/0.39
% 1.05/0.39 Contains.Choice.Funs: true
% 1.05/0.39 .....................
% 1.05/0.39
% 1.05/0.39 ********************************
% 1.05/0.39 * All subproblems solved! *
% 1.05/0.39 ********************************
% 1.05/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:544,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.05/0.39
% 1.05/0.39 %**** Beginning of derivation protocol ****
% 1.05/0.39 % SZS output start CNFRefutation
% See solution above
% 1.05/0.40
% 1.05/0.40 %**** End of derivation protocol ****
% 1.05/0.40 %**** no. of clauses in derivation: 545 ****
% 1.05/0.40 %**** clause counter: 544 ****
% 1.05/0.40
% 1.05/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:544,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------