%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU499^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:44:36 AM UTC 2026
% Result : Theorem 1.80s 0.61s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 17
% Syntax : Number of formulae : 517 ( 151 unt; 0 typ; 16 def)
% Number of atoms : 5006 (1460 equ; 0 cnn)
% Maximal formula atoms : 17 ( 9 avg)
% Number of connectives : 12885 (3222 ~;2050 |; 81 &;7336 @)
% ( 24 <=>; 172 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 276 ( 276 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 20 con; 0-4 aty)
% Number of variables : 2252 ( 56 ^;2135 !; 61 ?;2252 :)
% 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_exu,type,
exu: ( $i > $o ) > $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_replAx,type,
replAx: $o ).
thf(tp_sK10_SY216,type,
sK10_SY216: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK11_SY242,type,
sK11_SY242: $i > $i ).
thf(tp_sK12_SY243,type,
sK12_SY243: $i > ( $i > $o ) > $i ).
thf(tp_sK13_SY248,type,
sK13_SY248: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK14_SY249,type,
sK14_SY249: $i > $i > $i ).
thf(tp_sK15_SY216,type,
sK15_SY216: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK16_SY259,type,
sK16_SY259: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK17_SY216,type,
sK17_SY216: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK18_SY251,type,
sK18_SY251: $i > $i > $i > $i ).
thf(tp_sK19_SY251,type,
sK19_SY251: $i > $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i > $o ).
thf(tp_sK20_SY269,type,
sK20_SY269: $i > $i > $i > $i ).
thf(tp_sK21_SY280,type,
sK21_SY280: $i > $i > $i > $i ).
thf(tp_sK22_SY284,type,
sK22_SY284: $i > $i > $i > $i ).
thf(tp_sK23_SY276,type,
sK23_SY276: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK24_SY278,type,
sK24_SY278: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK2_SY178,type,
sK2_SY178: $i > $i ).
thf(tp_sK3_SY199,type,
sK3_SY199: $i > $i > $i ).
thf(tp_sK4_SY213,type,
sK4_SY213: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK5_SY200,type,
sK5_SY200: $i ).
thf(tp_sK6_SY149,type,
sK6_SY149: $i > $i > $i ).
thf(tp_sK7_SY162,type,
sK7_SY162: $i > $i ).
thf(tp_sK8_SY221,type,
sK8_SY221: $i > $i > $i ).
thf(tp_sK9_SY211,type,
sK9_SY211: $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/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(2,negated_conjecture,
( ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY23: $i > $i > $o,SY24: $i] :
( ! [SY25: $i] :
( ( in @ SY25 @ SY24 )
=> ? [SY27: $i] :
( ( SY23 @ SY25 @ SY27 )
& ! [SY28: $i] :
( ( SY23 @ SY25 @ SY28 )
=> ( SY27 = SY28 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY24 )
& ( SY23 @ 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 ) ) ) ) ) )
=> ( ! [SY55: $i > $o] :
( ? [SY57: $i] :
( ( SY55 @ SY57 )
& ! [SY58: $i] :
( ( SY55 @ SY58 )
=> ( SY57 = SY58 ) ) )
=> ( SY55
@ ( descr
@ ^ [Xx: $i] : ( SY55 @ 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 ) )
=> ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ? [Xx: $i] :
( ( SY0 @ Xx )
& ! [Xy: $i] :
( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,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,
( ( ! [SY23: $i > $i > $o,SY24: $i] :
( ! [SY25: $i] :
( ( in @ SY25 @ SY24 )
=> ? [SY27: $i] :
( ( SY23 @ SY25 @ SY27 )
& ! [SY28: $i] :
( ( SY23 @ SY25 @ SY28 )
=> ( SY27 = SY28 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY24 )
& ( SY23 @ 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,
( ( ! [SY55: $i > $o] :
( ? [SY57: $i] :
( ( SY55 @ SY57 )
& ! [SY58: $i] :
( ( SY55 @ SY58 )
=> ( SY57 = SY58 ) ) )
=> ( SY55
@ ( descr
@ ^ [Xx: $i] : ( SY55 @ 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,
( ( ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ? [Xx: $i] :
( ( SY0 @ Xx )
& ! [Xy: $i] :
( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ~ ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ? [Xx: $i] :
( ( SY0 @ Xx )
& ! [Xy: $i] :
( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(21,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(22,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(23,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(24,plain,
( ( ! [SY55: $i > $o] :
( ? [SY57: $i] :
( ( SY55 @ SY57 )
& ! [SY58: $i] :
( ( SY55 @ SY58 )
=> ( SY57 = SY58 ) ) )
=> ( SY55
@ ( descr
@ ^ [Xx: $i] : ( SY55 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(25,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(26,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(27,plain,
( ( ! [SY23: $i > $i > $o,SY24: $i] :
( ! [SY25: $i] :
( ( in @ SY25 @ SY24 )
=> ? [SY27: $i] :
( ( SY23 @ SY25 @ SY27 )
& ! [SY28: $i] :
( ( SY23 @ SY25 @ SY28 )
=> ( SY27 = SY28 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY24 )
& ( SY23 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(28,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(29,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(30,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(31,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(33,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(34,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(36,plain,
( ( ~ ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ? [Xx: $i] :
( ( SY0 @ Xx )
& ! [Xy: $i] :
( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(37,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(38,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)],[35,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(39,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)],[26,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(40,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)],[36,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(41,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)],[33,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(42,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(43,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)],[24,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(44,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)],[23,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(45,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)],[28,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(46,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)],[22,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(47,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)],[31,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(48,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)],[27,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(49,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)],[25,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(50,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)],[32,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(51,plain,
! [SV1: $i] :
( ( ~ ( in @ SV1 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(52,plain,
! [SV2: $i] :
( ( ~ ( in @ SV2 @ omega )
| ( in @ ( setadjoin @ SV2 @ SV2 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(53,plain,
! [SV3: $i] :
( ( ! [SY146: $i] :
( ~ ! [SY147: $i] :
~ ( ~ ( ~ ( in @ SY147 @ SV3 )
| ( in @ SY147 @ SY146 ) )
| ~ ( ~ ( in @ SY147 @ SY146 )
| ( in @ SY147 @ SV3 ) ) )
| ( SV3 = SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(54,plain,
! [SV4: $i] :
( ( ~ ~ ! [SY148: $i] :
~ ( in @ SY148 @ SV4 )
| ~ ! [SY149: $i] :
~ ~ ( ~ ( in @ SY149 @ SV4 )
| ~ ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( in @ SY150 @ SY149 )
| ~ ( in @ SY150 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(55,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV5: $i] :
( ( ! [SY151: $i,SY152: $i] :
~ ( ~ ( ~ ( in @ SY152 @ ( setadjoin @ SV5 @ SY151 ) )
| ( SY152 = SV5 )
| ( in @ SY152 @ SY151 ) )
| ~ ( ~ ( ( SY152 = SV5 )
| ( in @ SY152 @ SY151 ) )
| ( in @ SY152 @ ( setadjoin @ SV5 @ SY151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(57,plain,
! [SV6: $i] :
( ( ! [SY153: $i > $o,SY154: $i] :
( ~ ( in @ SY154
@ ( dsetconstr @ SV6
@ ^ [SX3: $i] : ( SY153 @ SX3 ) ) )
| ( SY153 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(58,plain,
! [SV7: $i > $o] :
( ( ~ ~ ! [SY156: $i] :
~ ~ ( ~ ( SV7 @ SY156 )
| ~ ! [SY157: $i] :
( ~ ( SV7 @ SY157 )
| ( SY156 = SY157 ) ) )
| ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(59,plain,
! [SV8: $i] :
( ( ! [SY159: $i > $o,SY160: $i] :
( ~ ( in @ SY160 @ SV8 )
| ~ ( SY159 @ SY160 )
| ( in @ SY160
@ ( dsetconstr @ SV8
@ ^ [SX3: $i] : ( SY159 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(60,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV9 )
| ~ ! [SY162: $i] :
( ~ ~ ( ~ ( in @ SY162 @ omega )
| ~ ( in @ SY162 @ SV9 ) )
| ( in @ ( setadjoin @ SY162 @ SY162 ) @ SV9 ) ) )
| ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(61,plain,
! [SV10: $i] :
( ( ! [SY164: $i > $o,SY165: $i] :
( ~ ( in @ SY165
@ ( dsetconstr @ SV10
@ ^ [SX3: $i] : ( SY164 @ SX3 ) ) )
| ( in @ SY165 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(62,plain,
! [SV11: $i] :
( ( ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ ( setunion @ SV11 ) )
| ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY167 @ SY168 )
| ~ ( in @ SY168 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( in @ SY167 @ SY169 )
| ~ ( in @ SY169 @ SV11 ) )
| ( in @ SY167 @ ( setunion @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(63,plain,
! [SV12: $i > $i > $o] :
( ( ! [SY170: $i] :
( ~ ! [SY171: $i] :
( ~ ( in @ SY171 @ SY170 )
| ~ ! [SY172: $i] :
~ ~ ( ~ ( SV12 @ SY171 @ SY172 )
| ~ ! [SY173: $i] :
( ~ ( SV12 @ SY171 @ SY173 )
| ( SY172 = SY173 ) ) ) )
| ~ ! [SY174: $i] :
~ ! [SY175: $i] :
~ ( ~ ( ~ ( in @ SY175 @ SY174 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ( in @ SY176 @ SY170 )
| ~ ( SV12 @ SY176 @ SY175 ) ) )
| ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ( in @ SY177 @ SY170 )
| ~ ( SV12 @ SY177 @ SY175 ) )
| ( in @ SY175 @ SY174 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(64,plain,
! [SV13: $i] :
( ( ~ ! [SY178: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY179: $i] :
( ~ ( in @ SY179 @ SY178 )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY179 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY181: $i,SY182: $i] :
( ~ ~ ( ~ ( in @ SY181 @ SV13 )
| ~ ( in @ SY182 @ SV13 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY178 )
| ~ ( ~ ( ~ ( in @ SY181 @ SX4 )
| ( in @ SY182 @ SX4 ) )
| ~ ( ~ ( in @ SY182 @ SX4 )
| ( in @ SY181 @ SX4 ) ) ) )
| ( SY181 = SY182 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY178 )
| ~ ( in @ SX3 @ SY178 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY188: $i] :
( ~ ~ ( ~ ! [SY189: $i] :
( ~ ( in @ SY189 @ SY188 )
| ( in @ SY189 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY188 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY178 )
| ~ ( in @ SX4 @ SY188 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY188 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY178 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(65,plain,
! [SV14: $i] :
( ( ! [SY196: $i] :
~ ( ~ ( ~ ( in @ SY196 @ ( powerset @ SV14 ) )
| ! [SY197: $i] :
( ~ ( in @ SY197 @ SY196 )
| ( in @ SY197 @ SV14 ) ) )
| ~ ( ~ ! [SY198: $i] :
( ~ ( in @ SY198 @ SY196 )
| ( in @ SY198 @ SV14 ) )
| ( in @ SY196 @ ( powerset @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(66,plain,
! [SV1: $i] :
( ( in @ SV1 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(67,plain,
! [SV2: $i] :
( ( ( ~ ( in @ SV2 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV2 @ SV2 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(68,plain,
! [SV15: $i,SV3: $i] :
( ( ~ ! [SY199: $i] :
~ ( ~ ( ~ ( in @ SY199 @ SV3 )
| ( in @ SY199 @ SV15 ) )
| ~ ( ~ ( in @ SY199 @ SV15 )
| ( in @ SY199 @ SV3 ) ) )
| ( SV3 = SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(69,plain,
! [SV4: $i] :
( ( ( ~ ~ ! [SY148: $i] :
~ ( in @ SY148 @ SV4 ) )
= $true )
| ( ( ~ ! [SY149: $i] :
~ ~ ( ~ ( in @ SY149 @ SV4 )
| ~ ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( in @ SY150 @ SY149 )
| ~ ( in @ SY150 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(70,plain,
( ( ~ ~ ! [SY200: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY200 )
| ~ ! [SY201: $i] :
( ~ ( sK1_SX0 @ SY201 )
| ( SY200 = SY201 ) ) )
| ~ ! [SY202: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY202 )
| ~ ! [SY203: $i] :
( ~ ( sK1_SX0 @ SY203 )
| ( SY202 = SY203 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(71,plain,
! [SV16: $i,SV5: $i] :
( ( ! [SY204: $i] :
~ ( ~ ( ~ ( in @ SY204 @ ( setadjoin @ SV5 @ SV16 ) )
| ( SY204 = SV5 )
| ( in @ SY204 @ SV16 ) )
| ~ ( ~ ( ( SY204 = SV5 )
| ( in @ SY204 @ SV16 ) )
| ( in @ SY204 @ ( setadjoin @ SV5 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(72,plain,
! [SV17: $i > $o,SV6: $i] :
( ( ! [SY205: $i] :
( ~ ( in @ SY205
@ ( dsetconstr @ SV6
@ ^ [SY206: $i] : ( SV17 @ SY206 ) ) )
| ( SV17 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(73,plain,
! [SV7: $i > $o] :
( ( ( ~ ~ ! [SY156: $i] :
~ ~ ( ~ ( SV7 @ SY156 )
| ~ ! [SY157: $i] :
( ~ ( SV7 @ SY157 )
| ( SY156 = SY157 ) ) ) )
= $true )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(74,plain,
! [SV18: $i > $o,SV8: $i] :
( ( ! [SY207: $i] :
( ~ ( in @ SY207 @ SV8 )
| ~ ( SV18 @ SY207 )
| ( in @ SY207
@ ( dsetconstr @ SV8
@ ^ [SY208: $i] : ( SV18 @ SY208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(75,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV9 )
| ~ ! [SY162: $i] :
( ~ ~ ( ~ ( in @ SY162 @ omega )
| ~ ( in @ SY162 @ SV9 ) )
| ( in @ ( setadjoin @ SY162 @ SY162 ) @ SV9 ) ) ) )
= $true )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(76,plain,
! [SV19: $i > $o,SV10: $i] :
( ( ! [SY209: $i] :
( ~ ( in @ SY209
@ ( dsetconstr @ SV10
@ ^ [SY210: $i] : ( SV19 @ SY210 ) ) )
| ( in @ SY209 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(77,plain,
! [SV11: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( in @ SV20 @ ( setunion @ SV11 ) )
| ~ ! [SY211: $i] :
~ ~ ( ~ ( in @ SV20 @ SY211 )
| ~ ( in @ SY211 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY212: $i] :
~ ~ ( ~ ( in @ SV20 @ SY212 )
| ~ ( in @ SY212 @ SV11 ) )
| ( in @ SV20 @ ( setunion @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(78,plain,
! [SV12: $i > $i > $o,SV21: $i] :
( ( ~ ! [SY213: $i] :
( ~ ( in @ SY213 @ SV21 )
| ~ ! [SY172: $i] :
~ ~ ( ~ ( SV12 @ SY213 @ SY172 )
| ~ ! [SY173: $i] :
( ~ ( SV12 @ SY213 @ SY173 )
| ( SY172 = SY173 ) ) ) )
| ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(79,plain,
! [SV13: $i] :
( ( ! [SY178: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY179: $i] :
( ~ ( in @ SY179 @ SY178 )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY179 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY181: $i,SY182: $i] :
( ~ ~ ( ~ ( in @ SY181 @ SV13 )
| ~ ( in @ SY182 @ SV13 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY178 )
| ~ ( ~ ( ~ ( in @ SY181 @ SX4 )
| ( in @ SY182 @ SX4 ) )
| ~ ( ~ ( in @ SY182 @ SX4 )
| ( in @ SY181 @ SX4 ) ) ) )
| ( SY181 = SY182 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY178 )
| ~ ( in @ SX3 @ SY178 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY188: $i] :
( ~ ~ ( ~ ! [SY189: $i] :
( ~ ( in @ SY189 @ SY188 )
| ( in @ SY189 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY188 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY178 )
| ~ ( in @ SX4 @ SY188 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY188 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY178 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV14: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( in @ SV22 @ ( powerset @ SV14 ) )
| ! [SY220: $i] :
( ~ ( in @ SY220 @ SV22 )
| ( in @ SY220 @ SV14 ) ) )
| ~ ( ~ ! [SY221: $i] :
( ~ ( in @ SY221 @ SV22 )
| ( in @ SY221 @ SV14 ) )
| ( in @ SV22 @ ( powerset @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
! [SV2: $i] :
( ( ( in @ SV2 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV2 @ SV2 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(82,plain,
! [SV15: $i,SV3: $i] :
( ( ( ~ ! [SY199: $i] :
~ ( ~ ( ~ ( in @ SY199 @ SV3 )
| ( in @ SY199 @ SV15 ) )
| ~ ( ~ ( in @ SY199 @ SV15 )
| ( in @ SY199 @ SV3 ) ) ) )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(83,plain,
! [SV4: $i] :
( ( ( ~ ! [SY148: $i] :
~ ( in @ SY148 @ SV4 ) )
= $false )
| ( ( ~ ! [SY149: $i] :
~ ~ ( ~ ( in @ SY149 @ SV4 )
| ~ ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( in @ SY150 @ SY149 )
| ~ ( in @ SY150 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(84,plain,
( ( ~ ~ ! [SY200: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY200 )
| ~ ! [SY201: $i] :
( ~ ( sK1_SX0 @ SY201 )
| ( SY200 = SY201 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(85,plain,
( ( ~ ! [SY202: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY202 )
| ~ ! [SY203: $i] :
( ~ ( sK1_SX0 @ SY203 )
| ( SY202 = SY203 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(86,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
| ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
| ~ ( ~ ( ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
| ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV17: $i > $o,SV6: $i,SV24: $i] :
( ( ~ ( in @ SV24
@ ( dsetconstr @ SV6
@ ^ [SY206: $i] : ( SV17 @ SY206 ) ) )
| ( SV17 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV7: $i > $o] :
( ( ( ~ ! [SY156: $i] :
~ ~ ( ~ ( SV7 @ SY156 )
| ~ ! [SY157: $i] :
( ~ ( SV7 @ SY157 )
| ( SY156 = SY157 ) ) ) )
= $false )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV18: $i > $o,SV8: $i,SV25: $i] :
( ( ~ ( in @ SV25 @ SV8 )
| ~ ( SV18 @ SV25 )
| ( in @ SV25
@ ( dsetconstr @ SV8
@ ^ [SY208: $i] : ( SV18 @ SY208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(90,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV9 )
| ~ ! [SY162: $i] :
( ~ ~ ( ~ ( in @ SY162 @ omega )
| ~ ( in @ SY162 @ SV9 ) )
| ( in @ ( setadjoin @ SY162 @ SY162 ) @ SV9 ) ) ) )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(91,plain,
! [SV19: $i > $o,SV10: $i,SV26: $i] :
( ( ~ ( in @ SV26
@ ( dsetconstr @ SV10
@ ^ [SY210: $i] : ( SV19 @ SY210 ) ) )
| ( in @ SV26 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(92,plain,
! [SV11: $i,SV20: $i] :
( ( ~ ( ~ ( in @ SV20 @ ( setunion @ SV11 ) )
| ~ ! [SY211: $i] :
~ ~ ( ~ ( in @ SV20 @ SY211 )
| ~ ( in @ SY211 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY212: $i] :
~ ~ ( ~ ( in @ SV20 @ SY212 )
| ~ ( in @ SY212 @ SV11 ) )
| ( in @ SV20 @ ( setunion @ SV11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(93,plain,
! [SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ! [SY213: $i] :
( ~ ( in @ SY213 @ SV21 )
| ~ ! [SY172: $i] :
~ ~ ( ~ ( SV12 @ SY213 @ SY172 )
| ~ ! [SY173: $i] :
( ~ ( SV12 @ SY213 @ SY173 )
| ( SY172 = SY173 ) ) ) ) )
= $true )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(94,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ~ ( ~ ( in @ SY230 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY231 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY230 )
| ( in @ SX4 @ SY231 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY231 )
| ( in @ SX4 @ SY230 ) ) ) )
| ~ ! [SY234: $i] :
( ~ ~ ( ~ ! [SY189: $i] :
( ~ ( in @ SY189 @ SY234 )
| ( in @ SY189 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY234 ) )
| ~ ! [SY237: $i] :
~ ~ ! [SY238: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY237 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY238 @ SY234 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY237 )
| ~ ( in @ SX5 @ SY234 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY237 ) )
| ( in @ SY238 @ SY240 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(95,plain,
! [SV14: $i,SV22: $i] :
( ( ~ ( ~ ( in @ SV22 @ ( powerset @ SV14 ) )
| ! [SY220: $i] :
( ~ ( in @ SY220 @ SV22 )
| ( in @ SY220 @ SV14 ) ) )
| ~ ( ~ ! [SY221: $i] :
( ~ ( in @ SY221 @ SV22 )
| ( in @ SY221 @ SV14 ) )
| ( in @ SV22 @ ( powerset @ SV14 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV15: $i,SV3: $i] :
( ( ( ! [SY199: $i] :
~ ( ~ ( ~ ( in @ SY199 @ SV3 )
| ( in @ SY199 @ SV15 ) )
| ~ ( ~ ( in @ SY199 @ SV15 )
| ( in @ SY199 @ SV3 ) ) ) )
= $false )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(97,plain,
! [SV4: $i] :
( ( ( ! [SY148: $i] :
~ ( in @ SY148 @ SV4 ) )
= $true )
| ( ( ~ ! [SY149: $i] :
~ ~ ( ~ ( in @ SY149 @ SV4 )
| ~ ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( in @ SY150 @ SY149 )
| ~ ( in @ SY150 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(98,plain,
( ( ~ ! [SY200: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY200 )
| ~ ! [SY201: $i] :
( ~ ( sK1_SX0 @ SY201 )
| ( SY200 = SY201 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(99,plain,
( ( ! [SY202: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY202 )
| ~ ! [SY203: $i] :
( ~ ( sK1_SX0 @ SY203 )
| ( SY202 = SY203 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(100,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ~ ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
| ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
| ~ ( ~ ( ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
| ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV17: $i > $o,SV6: $i,SV24: $i] :
( ( ( ~ ( in @ SV24
@ ( dsetconstr @ SV6
@ ^ [SY206: $i] : ( SV17 @ SY206 ) ) ) )
= $true )
| ( ( SV17 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV7: $i > $o] :
( ( ( ! [SY156: $i] :
~ ~ ( ~ ( SV7 @ SY156 )
| ~ ! [SY157: $i] :
( ~ ( SV7 @ SY157 )
| ( SY156 = SY157 ) ) ) )
= $true )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(103,plain,
! [SV18: $i > $o,SV8: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV8 ) )
= $true )
| ( ( ~ ( SV18 @ SV25 )
| ( in @ SV25
@ ( dsetconstr @ SV8
@ ^ [SY208: $i] : ( SV18 @ SY208 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV9: $i] :
( ( ( ~ ( in @ emptyset @ SV9 )
| ~ ! [SY162: $i] :
( ~ ~ ( ~ ( in @ SY162 @ omega )
| ~ ( in @ SY162 @ SV9 ) )
| ( in @ ( setadjoin @ SY162 @ SY162 ) @ SV9 ) ) )
= $true )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(105,plain,
! [SV19: $i > $o,SV10: $i,SV26: $i] :
( ( ( ~ ( in @ SV26
@ ( dsetconstr @ SV10
@ ^ [SY210: $i] : ( SV19 @ SY210 ) ) ) )
= $true )
| ( ( in @ SV26 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV11: $i,SV20: $i] :
( ( ~ ( ~ ( in @ SV20 @ ( setunion @ SV11 ) )
| ~ ! [SY211: $i] :
~ ~ ( ~ ( in @ SV20 @ SY211 )
| ~ ( in @ SY211 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(107,plain,
! [SV11: $i,SV20: $i] :
( ( ~ ( ~ ~ ! [SY212: $i] :
~ ~ ( ~ ( in @ SV20 @ SY212 )
| ~ ( in @ SY212 @ SV11 ) )
| ( in @ SV20 @ ( setunion @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(108,plain,
! [SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY213: $i] :
( ~ ( in @ SY213 @ SV21 )
| ~ ! [SY172: $i] :
~ ~ ( ~ ( SV12 @ SY213 @ SY172 )
| ~ ! [SY173: $i] :
( ~ ( SV12 @ SY213 @ SY173 )
| ( SY172 = SY173 ) ) ) ) )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV13: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ~ ( ~ ( in @ SY230 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY231 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY230 )
| ( in @ SX4 @ SY231 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY231 )
| ( in @ SX4 @ SY230 ) ) ) )
| ~ ! [SY234: $i] :
( ~ ~ ( ~ ! [SY189: $i] :
( ~ ( in @ SY189 @ SY234 )
| ( in @ SY189 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY234 ) )
| ~ ! [SY237: $i] :
~ ~ ! [SY238: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY237 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY238 @ SY234 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY237 )
| ~ ( in @ SX5 @ SY234 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY237 ) )
| ( in @ SY238 @ SY240 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(110,plain,
! [SV14: $i,SV22: $i] :
( ( ~ ( ~ ( in @ SV22 @ ( powerset @ SV14 ) )
| ! [SY220: $i] :
( ~ ( in @ SY220 @ SV22 )
| ( in @ SY220 @ SV14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(111,plain,
! [SV14: $i,SV22: $i] :
( ( ~ ( ~ ! [SY221: $i] :
( ~ ( in @ SY221 @ SV22 )
| ( in @ SY221 @ SV14 ) )
| ( in @ SV22 @ ( powerset @ SV14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(112,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 ) )
| ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) ) ) )
= $false )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[96]) ).
thf(113,plain,
! [SV4: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV4 ) )
= $true )
| ( ( ~ ! [SY149: $i] :
~ ~ ( ~ ( in @ SY149 @ SV4 )
| ~ ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( in @ SY150 @ SY149 )
| ~ ( in @ SY150 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(114,plain,
( ( ! [SY200: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY200 )
| ~ ! [SY201: $i] :
( ~ ( sK1_SX0 @ SY201 )
| ( SY200 = SY201 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(115,plain,
! [SV28: $i] :
( ( ~ ~ ( ~ ( sK1_SX0 @ SV28 )
| ~ ! [SY242: $i] :
( ~ ( sK1_SX0 @ SY242 )
| ( SV28 = SY242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(116,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ~ ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
| ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(117,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ~ ( ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
| ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(118,plain,
! [SV17: $i > $o,SV6: $i,SV24: $i] :
( ( ( in @ SV24
@ ( dsetconstr @ SV6
@ ^ [SY206: $i] : ( SV17 @ SY206 ) ) )
= $false )
| ( ( SV17 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(119,plain,
! [SV29: $i,SV7: $i > $o] :
( ( ( ~ ~ ( ~ ( SV7 @ SV29 )
| ~ ! [SY243: $i] :
( ~ ( SV7 @ SY243 )
| ( SV29 = SY243 ) ) ) )
= $true )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV18: $i > $o,SV8: $i,SV25: $i] :
( ( ( in @ SV25 @ SV8 )
= $false )
| ( ( ~ ( SV18 @ SV25 )
| ( in @ SV25
@ ( dsetconstr @ SV8
@ ^ [SY208: $i] : ( SV18 @ SY208 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(121,plain,
! [SV9: $i] :
( ( ( ~ ( in @ emptyset @ SV9 ) )
= $true )
| ( ( ~ ! [SY162: $i] :
( ~ ~ ( ~ ( in @ SY162 @ omega )
| ~ ( in @ SY162 @ SV9 ) )
| ( in @ ( setadjoin @ SY162 @ SY162 ) @ SV9 ) ) )
= $true )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(122,plain,
! [SV19: $i > $o,SV10: $i,SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ SV10
@ ^ [SY210: $i] : ( SV19 @ SY210 ) ) )
= $false )
| ( ( in @ SV26 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(123,plain,
! [SV11: $i,SV20: $i] :
( ( ~ ( in @ SV20 @ ( setunion @ SV11 ) )
| ~ ! [SY211: $i] :
~ ~ ( ~ ( in @ SV20 @ SY211 )
| ~ ( in @ SY211 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(124,plain,
! [SV11: $i,SV20: $i] :
( ( ~ ~ ! [SY212: $i] :
~ ~ ( ~ ( in @ SV20 @ SY212 )
| ~ ( in @ SY212 @ SV11 ) )
| ( in @ SV20 @ ( setunion @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(125,plain,
! [SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
| ~ ! [SY244: $i] :
~ ~ ( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY244 )
| ~ ! [SY245: $i] :
( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY245 )
| ( SY244 = SY245 ) ) ) )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(126,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ~ ( ~ ( in @ SY230 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY231 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY230 )
| ( in @ SX4 @ SY231 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY231 )
| ( in @ SX4 @ SY230 ) ) ) )
| ~ ! [SY234: $i] :
( ~ ~ ( ~ ! [SY189: $i] :
( ~ ( in @ SY189 @ SY234 )
| ( in @ SY189 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY234 ) )
| ~ ! [SY237: $i] :
~ ~ ! [SY238: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY237 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY238 @ SY234 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY237 )
| ~ ( in @ SX5 @ SY234 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY237 ) )
| ( in @ SY238 @ SY240 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(127,plain,
! [SV14: $i,SV22: $i] :
( ( ~ ( in @ SV22 @ ( powerset @ SV14 ) )
| ! [SY220: $i] :
( ~ ( in @ SY220 @ SV22 )
| ( in @ SY220 @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(128,plain,
! [SV14: $i,SV22: $i] :
( ( ~ ! [SY221: $i] :
( ~ ( in @ SY221 @ SV22 )
| ( in @ SY221 @ SV14 ) )
| ( in @ SV22 @ ( powerset @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(129,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 ) )
| ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(130,plain,
! [SV4: $i,SV27: $i] :
( ( ( in @ SV27 @ SV4 )
= $false )
| ( ( ~ ! [SY149: $i] :
~ ~ ( ~ ( in @ SY149 @ SV4 )
| ~ ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( in @ SY150 @ SY149 )
| ~ ( in @ SY150 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(131,plain,
( ( ~ ~ ( ~ ( sK1_SX0 @ sK5_SY200 )
| ~ ! [SY246: $i] :
( ~ ( sK1_SX0 @ SY246 )
| ( sK5_SY200 = SY246 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(132,plain,
! [SV28: $i] :
( ( ~ ( ~ ( sK1_SX0 @ SV28 )
| ~ ! [SY242: $i] :
( ~ ( sK1_SX0 @ SY242 )
| ( SV28 = SY242 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(133,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
| ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(134,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
| ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(135,plain,
! [SV29: $i,SV7: $i > $o] :
( ( ( ~ ( ~ ( SV7 @ SV29 )
| ~ ! [SY243: $i] :
( ~ ( SV7 @ SY243 )
| ( SV29 = SY243 ) ) ) )
= $false )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV8: $i,SV25: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ SV25 ) )
= $true )
| ( ( in @ SV25
@ ( dsetconstr @ SV8
@ ^ [SY208: $i] : ( SV18 @ SY208 ) ) )
= $true )
| ( ( in @ SV25 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV9: $i] :
( ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ~ ! [SY162: $i] :
( ~ ~ ( ~ ( in @ SY162 @ omega )
| ~ ( in @ SY162 @ SV9 ) )
| ( in @ ( setadjoin @ SY162 @ SY162 ) @ SV9 ) ) )
= $true )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(138,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ ( setunion @ SV11 ) ) )
= $true )
| ( ( ~ ! [SY211: $i] :
~ ~ ( ~ ( in @ SV20 @ SY211 )
| ~ ( in @ SY211 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(139,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ~ ! [SY212: $i] :
~ ~ ( ~ ( in @ SV20 @ SY212 )
| ~ ( in @ SY212 @ SV11 ) ) )
= $true )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(140,plain,
! [SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 ) )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(141,plain,
! [SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ! [SY244: $i] :
~ ~ ( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY244 )
| ~ ! [SY245: $i] :
( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY245 )
| ( SY244 = SY245 ) ) ) )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(142,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ~ ( ~ ( in @ SY230 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY231 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY230 )
| ( in @ SX4 @ SY231 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY231 )
| ( in @ SX4 @ SY230 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(143,plain,
! [SV13: $i] :
( ( ~ ! [SY234: $i] :
( ~ ~ ( ~ ! [SY189: $i] :
( ~ ( in @ SY189 @ SY234 )
| ( in @ SY189 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY234 ) )
| ~ ! [SY237: $i] :
~ ~ ! [SY238: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY237 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY238 @ SY234 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY237 )
| ~ ( in @ SX5 @ SY234 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY237 ) )
| ( in @ SY238 @ SY240 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(144,plain,
! [SV14: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( in @ SY220 @ SV22 )
| ( in @ SY220 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(145,plain,
! [SV14: $i,SV22: $i] :
( ( ( ~ ! [SY221: $i] :
( ~ ( in @ SY221 @ SV22 )
| ( in @ SY221 @ SV14 ) ) )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(146,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(147,plain,
! [SV27: $i,SV4: $i] :
( ( ( ! [SY149: $i] :
~ ~ ( ~ ( in @ SY149 @ SV4 )
| ~ ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( in @ SY150 @ SY149 )
| ~ ( in @ SY150 @ SV4 ) ) ) )
= $false )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(148,plain,
( ( ~ ( ~ ( sK1_SX0 @ sK5_SY200 )
| ~ ! [SY246: $i] :
( ~ ( sK1_SX0 @ SY246 )
| ( sK5_SY200 = SY246 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(149,plain,
! [SV28: $i] :
( ( ~ ( sK1_SX0 @ SV28 )
| ~ ! [SY242: $i] :
( ~ ( sK1_SX0 @ SY242 )
| ( SV28 = SY242 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(150,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) ) )
= $true )
| ( ( ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(151,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) ) )
= $true )
| ( ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(152,plain,
! [SV29: $i,SV7: $i > $o] :
( ( ( ~ ( SV7 @ SV29 )
| ~ ! [SY243: $i] :
( ~ ( SV7 @ SY243 )
| ( SV29 = SY243 ) ) )
= $true )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(153,plain,
! [SV8: $i,SV25: $i,SV18: $i > $o] :
( ( ( SV18 @ SV25 )
= $false )
| ( ( in @ SV25
@ ( dsetconstr @ SV8
@ ^ [SY208: $i] : ( SV18 @ SY208 ) ) )
= $true )
| ( ( in @ SV25 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(154,plain,
! [SV9: $i] :
( ( ( ! [SY162: $i] :
( ~ ~ ( ~ ( in @ SY162 @ omega )
| ~ ( in @ SY162 @ SV9 ) )
| ( in @ ( setadjoin @ SY162 @ SY162 ) @ SV9 ) ) )
= $false )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(155,plain,
! [SV11: $i,SV20: $i] :
( ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $false )
| ( ( ~ ! [SY211: $i] :
~ ~ ( ~ ( in @ SV20 @ SY211 )
| ~ ( in @ SY211 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(156,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ! [SY212: $i] :
~ ~ ( ~ ( in @ SV20 @ SY212 )
| ~ ( in @ SY212 @ SV11 ) ) )
= $false )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(157,plain,
! [SV21: $i,SV12: $i > $i > $o] :
( ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(158,plain,
! [SV21: $i,SV12: $i > $i > $o] :
( ( ( ! [SY244: $i] :
~ ~ ( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY244 )
| ~ ! [SY245: $i] :
( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY245 )
| ( SY244 = SY245 ) ) ) )
= $true )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(159,plain,
! [SV13: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ~ ( ~ ( in @ SY230 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY231 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY230 )
| ( in @ SX4 @ SY231 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY231 )
| ( in @ SX4 @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(160,plain,
! [SV13: $i] :
( ( ! [SY234: $i] :
( ~ ~ ( ~ ! [SY189: $i] :
( ~ ( in @ SY189 @ SY234 )
| ( in @ SY189 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY234 ) )
| ~ ! [SY237: $i] :
~ ~ ! [SY238: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY237 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY238 @ SY234 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY237 )
| ~ ( in @ SX5 @ SY234 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY237 ) )
| ( in @ SY238 @ SY240 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(161,plain,
! [SV14: $i,SV22: $i] :
( ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $false )
| ( ( ! [SY220: $i] :
( ~ ( in @ SY220 @ SV22 )
| ( in @ SY220 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(162,plain,
! [SV14: $i,SV22: $i] :
( ( ( ! [SY221: $i] :
( ~ ( in @ SY221 @ SV22 )
| ( in @ SY221 @ SV14 ) ) )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(163,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(164,plain,
! [SV4: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY149 @ SV27 @ SV4 ) @ SV4 )
| ~ ~ ~ ! [SY247: $i] :
~ ~ ( ~ ( in @ SY247 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SY247 @ SV4 ) ) ) )
= $false )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[147]) ).
thf(165,plain,
( ( ~ ( sK1_SX0 @ sK5_SY200 )
| ~ ! [SY246: $i] :
( ~ ( sK1_SX0 @ SY246 )
| ( sK5_SY200 = SY246 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(166,plain,
! [SV28: $i] :
( ( ( ~ ( sK1_SX0 @ SV28 ) )
= $true )
| ( ( ~ ! [SY242: $i] :
( ~ ( sK1_SX0 @ SY242 )
| ( SV28 = SY242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(167,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
= $false )
| ( ( ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(168,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( ( SV23 = SV5 )
| ( in @ SV23 @ SV16 ) )
= $false )
| ( ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(169,plain,
! [SV29: $i,SV7: $i > $o] :
( ( ( ~ ( SV7 @ SV29 ) )
= $true )
| ( ( ~ ! [SY243: $i] :
( ~ ( SV7 @ SY243 )
| ( SV29 = SY243 ) ) )
= $true )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(170,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY162 @ SV9 ) @ omega )
| ~ ( in @ ( sK7_SY162 @ SV9 ) @ SV9 ) )
| ( in @ ( setadjoin @ ( sK7_SY162 @ SV9 ) @ ( sK7_SY162 @ SV9 ) ) @ SV9 ) )
= $false )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[154]) ).
thf(171,plain,
! [SV11: $i,SV20: $i] :
( ( ( ! [SY211: $i] :
~ ~ ( ~ ( in @ SV20 @ SY211 )
| ~ ( in @ SY211 @ SV11 ) ) )
= $false )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(172,plain,
! [SV11: $i,SV20: $i] :
( ( ( ! [SY212: $i] :
~ ~ ( ~ ( in @ SV20 @ SY212 )
| ~ ( in @ SY212 @ SV11 ) ) )
= $true )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(173,plain,
! [SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(174,plain,
! [SV30: $i,SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
| ~ ! [SY248: $i] :
( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY248 )
| ( SV30 = SY248 ) ) ) )
= $true )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(175,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ~ ( ~ ( in @ SY230 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY231 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY230 )
| ( in @ SX4 @ SY231 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY231 )
| ( in @ SX4 @ SY230 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(176,plain,
! [SV13: $i,SV31: $i] :
( ( ~ ~ ( ~ ! [SY249: $i] :
( ~ ( in @ SY249 @ SV31 )
| ( in @ SY249 @ SV13 ) )
| ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
| ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(177,plain,
! [SV14: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV22 )
| ( in @ SV32 @ SV14 ) )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(178,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK8_SY221 @ SV14 @ SV22 ) @ SV22 )
| ( in @ ( sK8_SY221 @ SV14 @ SV22 ) @ SV14 ) )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[162]) ).
thf(179,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(180,plain,
! [SV3: $i,SV15: $i] :
( ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(181,plain,
! [SV4: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY149 @ SV27 @ SV4 ) @ SV4 )
| ~ ~ ~ ! [SY247: $i] :
~ ~ ( ~ ( in @ SY247 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SY247 @ SV4 ) ) ) )
= $true )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(182,plain,
( ( ~ ( sK1_SX0 @ sK5_SY200 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(183,plain,
( ( ~ ! [SY246: $i] :
( ~ ( sK1_SX0 @ SY246 )
| ( sK5_SY200 = SY246 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(184,plain,
! [SV28: $i] :
( ( ( sK1_SX0 @ SV28 )
= $false )
| ( ( ~ ! [SY242: $i] :
( ~ ( sK1_SX0 @ SY242 )
| ( SV28 = SY242 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(185,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( SV23 = SV5 )
= $true )
| ( ( in @ SV23 @ SV16 )
= $true )
| ( ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(186,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( SV23 = SV5 )
= $false )
| ( ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(187,plain,
! [SV5: $i,SV16: $i,SV23: $i] :
( ( ( in @ SV23 @ SV16 )
= $false )
| ( ( in @ SV23 @ ( setadjoin @ SV5 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(188,plain,
! [SV29: $i,SV7: $i > $o] :
( ( ( SV7 @ SV29 )
= $false )
| ( ( ~ ! [SY243: $i] :
( ~ ( SV7 @ SY243 )
| ( SV29 = SY243 ) ) )
= $true )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(189,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY162 @ SV9 ) @ omega )
| ~ ( in @ ( sK7_SY162 @ SV9 ) @ SV9 ) ) )
= $false )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(190,plain,
! [SV9: $i] :
( ( ( in @ ( setadjoin @ ( sK7_SY162 @ SV9 ) @ ( sK7_SY162 @ SV9 ) ) @ SV9 )
= $false )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(191,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ SV20 @ ( sK9_SY211 @ SV11 @ SV20 ) )
| ~ ( in @ ( sK9_SY211 @ SV11 @ SV20 ) @ SV11 ) ) )
= $false )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[171]) ).
thf(192,plain,
! [SV11: $i,SV33: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ SV20 @ SV33 )
| ~ ( in @ SV33 @ SV11 ) ) )
= $true )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(193,plain,
! [SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ! [SY256: $i] :
~ ( ~ ( ~ ( in @ SY256 @ ( sK10_SY216 @ SV12 @ SV21 ) )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY256 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY256 ) )
| ( in @ SY256 @ ( sK10_SY216 @ SV12 @ SV21 ) ) ) ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[173]) ).
thf(194,plain,
! [SV30: $i,SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
| ~ ! [SY248: $i] :
( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY248 )
| ( SV30 = SY248 ) ) ) )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(195,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(196,plain,
! [SV13: $i] :
( ( ~ ! [SY230: $i,SY231: $i] :
( ~ ~ ( ~ ( in @ SY230 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY231 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY230 )
| ( in @ SX4 @ SY231 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY231 )
| ( in @ SX4 @ SY230 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(197,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ! [SY249: $i] :
( ~ ( in @ SY249 @ SV31 )
| ( in @ SY249 @ SV13 ) )
| ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) ) )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(198,plain,
! [SV14: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV22 ) )
= $true )
| ( ( in @ SV32 @ SV14 )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(199,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK8_SY221 @ SV14 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(200,plain,
! [SV22: $i,SV14: $i] :
( ( ( in @ ( sK8_SY221 @ SV14 @ SV22 ) @ SV14 )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(201,plain,
! [SV3: $i,SV15: $i] :
( ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(202,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
= $false )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(203,plain,
! [SV4: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK6_SY149 @ SV27 @ SV4 ) @ SV4 )
| ~ ~ ~ ! [SY247: $i] :
~ ~ ( ~ ( in @ SY247 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SY247 @ SV4 ) ) )
= $false )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(204,plain,
( ( sK1_SX0 @ sK5_SY200 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(205,plain,
( ( ! [SY246: $i] :
( ~ ( sK1_SX0 @ SY246 )
| ( sK5_SY200 = SY246 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(206,plain,
! [SV28: $i] :
( ( ( ! [SY242: $i] :
( ~ ( sK1_SX0 @ SY242 )
| ( SV28 = SY242 ) ) )
= $false )
| ( ( sK1_SX0 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(207,plain,
! [SV29: $i,SV7: $i > $o] :
( ( ( ! [SY243: $i] :
( ~ ( SV7 @ SY243 )
| ( SV29 = SY243 ) ) )
= $false )
| ( ( SV7 @ SV29 )
= $false )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(208,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY162 @ SV9 ) @ omega )
| ~ ( in @ ( sK7_SY162 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(209,plain,
! [SV9: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ omega )
| ( in @ SV34 @ SV9 ) )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( in @ ( setadjoin @ ( sK7_SY162 @ SV9 ) @ ( sK7_SY162 @ SV9 ) ) @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(210,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ SV20 @ ( sK9_SY211 @ SV11 @ SV20 ) )
| ~ ( in @ ( sK9_SY211 @ SV11 @ SV20 ) @ SV11 ) ) )
= $true )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(211,plain,
! [SV11: $i,SV33: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ SV20 @ SV33 )
| ~ ( in @ SV33 @ SV11 ) ) )
= $false )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(212,plain,
! [SV21: $i,SV12: $i > $i > $o] :
( ( ( ! [SY256: $i] :
~ ( ~ ( ~ ( in @ SY256 @ ( sK10_SY216 @ SV12 @ SV21 ) )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY256 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY256 ) )
| ( in @ SY256 @ ( sK10_SY216 @ SV12 @ SV21 ) ) ) ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(213,plain,
! [SV30: $i,SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
| ~ ! [SY248: $i] :
( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY248 )
| ( SV30 = SY248 ) ) )
= $true )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(214,plain,
! [SV13: $i] :
( ( ~ ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(215,plain,
! [SV13: $i] :
( ( ! [SY230: $i,SY231: $i] :
( ~ ~ ( ~ ( in @ SY230 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY231 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY230 )
| ( in @ SX4 @ SY231 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY231 )
| ( in @ SX4 @ SY230 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(216,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ( ~ ! [SY249: $i] :
( ~ ( in @ SY249 @ SV31 )
| ( in @ SY249 @ SV13 ) )
| ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(217,plain,
! [SV14: $i,SV22: $i,SV32: $i] :
( ( ( in @ SV32 @ SV22 )
= $false )
| ( ( in @ SV32 @ SV14 )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(218,plain,
! [SV22: $i,SV14: $i] :
( ( ( in @ ( sK8_SY221 @ SV14 @ SV22 ) @ SV22 )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(219,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
| ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(220,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
= $false )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(221,plain,
! [SV3: $i,SV15: $i] :
( ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
= $false )
| ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
= $false )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(222,plain,
! [SV4: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK6_SY149 @ SV27 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(223,plain,
! [SV4: $i,SV27: $i] :
( ( ( ~ ~ ~ ! [SY247: $i] :
~ ~ ( ~ ( in @ SY247 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SY247 @ SV4 ) ) )
= $false )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(224,plain,
! [SV35: $i] :
( ( ~ ( sK1_SX0 @ SV35 )
| ( sK5_SY200 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(225,plain,
! [SV28: $i] :
( ( ( ~ ( sK1_SX0 @ ( sK11_SY242 @ SV28 ) )
| ( SV28
= ( sK11_SY242 @ SV28 ) ) )
= $false )
| ( ( sK1_SX0 @ SV28 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[206]) ).
thf(226,plain,
! [SV29: $i,SV7: $i > $o] :
( ( ( ~ ( SV7 @ ( sK12_SY243 @ SV29 @ SV7 ) )
| ( SV29
= ( sK12_SY243 @ SV29 @ SV7 ) ) )
= $false )
| ( ( SV7 @ SV29 )
= $false )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[207]) ).
thf(227,plain,
! [SV9: $i] :
( ( ( ~ ( in @ ( sK7_SY162 @ SV9 ) @ omega )
| ~ ( in @ ( sK7_SY162 @ SV9 ) @ SV9 ) )
= $false )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(228,plain,
! [SV9: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ omega ) )
= $true )
| ( ( in @ SV34 @ SV9 )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( in @ ( setadjoin @ ( sK7_SY162 @ SV9 ) @ ( sK7_SY162 @ SV9 ) ) @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(229,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ ( sK9_SY211 @ SV11 @ SV20 ) )
| ~ ( in @ ( sK9_SY211 @ SV11 @ SV20 ) @ SV11 ) )
= $false )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(230,plain,
! [SV11: $i,SV33: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV33 )
| ~ ( in @ SV33 @ SV11 ) )
= $true )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(231,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV21 )
| ~ ( SV12 @ SY259 @ SV36 ) ) )
| ~ ( ~ ~ ! [SY260: $i] :
~ ~ ( ~ ( in @ SY260 @ SV21 )
| ~ ( SV12 @ SY260 @ SV36 ) )
| ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) ) ) ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(232,plain,
! [SV30: $i,SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 ) )
= $true )
| ( ( ~ ! [SY248: $i] :
( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY248 )
| ( SV30 = SY248 ) ) )
= $true )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(233,plain,
! [SV13: $i] :
( ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) )
| ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(234,plain,
! [SV13: $i,SV37: $i] :
( ( ! [SY261: $i] :
( ~ ~ ( ~ ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY261 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SY262: $i] :
( ~ ( in @ SY262 @ SV37 )
| ( in @ SY262 @ SY261 ) )
| ! [SY263: $i] :
( ~ ( in @ SY263 @ SY261 )
| ( in @ SY263 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(235,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ! [SY249: $i] :
( ~ ( in @ SY249 @ SV31 )
| ( in @ SY249 @ SV13 ) )
| ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(236,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(237,plain,
! [SV3: $i,SV15: $i] :
( ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
= $false )
| ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(238,plain,
! [SV3: $i,SV15: $i] :
( ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
= $true )
| ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
= $false )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(239,plain,
! [SV4: $i,SV27: $i] :
( ( ( in @ ( sK6_SY149 @ SV27 @ SV4 ) @ SV4 )
= $true )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(240,plain,
! [SV4: $i,SV27: $i] :
( ( ( ~ ~ ! [SY247: $i] :
~ ~ ( ~ ( in @ SY247 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SY247 @ SV4 ) ) )
= $true )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(241,plain,
! [SV35: $i] :
( ( ( ~ ( sK1_SX0 @ SV35 ) )
= $true )
| ( ( sK5_SY200 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(242,plain,
! [SV28: $i] :
( ( ( ~ ( sK1_SX0 @ ( sK11_SY242 @ SV28 ) ) )
= $false )
| ( ( sK1_SX0 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(243,plain,
! [SV28: $i] :
( ( ( SV28
= ( sK11_SY242 @ SV28 ) )
= $false )
| ( ( sK1_SX0 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(244,plain,
! [SV29: $i,SV7: $i > $o] :
( ( ( ~ ( SV7 @ ( sK12_SY243 @ SV29 @ SV7 ) ) )
= $false )
| ( ( SV7 @ SV29 )
= $false )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(245,plain,
! [SV7: $i > $o,SV29: $i] :
( ( ( SV29
= ( sK12_SY243 @ SV29 @ SV7 ) )
= $false )
| ( ( SV7 @ SV29 )
= $false )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(246,plain,
! [SV9: $i] :
( ( ( ~ ( in @ ( sK7_SY162 @ SV9 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(247,plain,
! [SV9: $i] :
( ( ( ~ ( in @ ( sK7_SY162 @ SV9 ) @ SV9 ) )
= $false )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(248,plain,
! [SV9: $i,SV34: $i] :
( ( ( in @ SV34 @ omega )
= $false )
| ( ( in @ SV34 @ SV9 )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( in @ ( setadjoin @ ( sK7_SY162 @ SV9 ) @ ( sK7_SY162 @ SV9 ) ) @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(249,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ ( sK9_SY211 @ SV11 @ SV20 ) ) )
= $false )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(250,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK9_SY211 @ SV11 @ SV20 ) @ SV11 ) )
= $false )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(251,plain,
! [SV11: $i,SV33: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV33 ) )
= $true )
| ( ( ~ ( in @ SV33 @ SV11 ) )
= $true )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(252,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( ~ ( ~ ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV21 )
| ~ ( SV12 @ SY259 @ SV36 ) ) )
| ~ ( ~ ~ ! [SY260: $i] :
~ ~ ( ~ ( in @ SY260 @ SV21 )
| ~ ( SV12 @ SY260 @ SV36 ) )
| ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(253,plain,
! [SV30: $i,SV21: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( ~ ! [SY248: $i] :
( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY248 )
| ( SV30 = SY248 ) ) )
= $true )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(254,plain,
! [SV13: $i] :
( ( ~ ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(255,plain,
! [SV13: $i] :
( ( ~ ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(256,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ~ ~ ( ~ ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SV38 @ ( sK2_SY178 @ SV13 ) ) )
| ! [SY264: $i] :
( ~ ( in @ SY264 @ SV37 )
| ( in @ SY264 @ SV38 ) )
| ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(257,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ! [SY249: $i] :
( ~ ( in @ SY249 @ SV31 )
| ( in @ SY249 @ SV13 ) ) )
= $true )
| ( ( ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(258,plain,
! [SV3: $i,SV15: $i] :
( ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV15 )
= $true )
| ( ( in @ ( sK3_SY199 @ SV15 @ SV3 ) @ SV3 )
= $true )
| ( ( SV3 = SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(259,plain,
! [SV4: $i,SV27: $i] :
( ( ( ~ ! [SY247: $i] :
~ ~ ( ~ ( in @ SY247 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SY247 @ SV4 ) ) )
= $false )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(260,plain,
! [SV35: $i] :
( ( ( sK1_SX0 @ SV35 )
= $false )
| ( ( sK5_SY200 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(261,plain,
! [SV28: $i] :
( ( ( sK1_SX0 @ ( sK11_SY242 @ SV28 ) )
= $true )
| ( ( sK1_SX0 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(262,plain,
! [SV29: $i,SV7: $i > $o] :
( ( ( SV7 @ ( sK12_SY243 @ SV29 @ SV7 ) )
= $true )
| ( ( SV7 @ SV29 )
= $false )
| ( ( SV7
@ ( descr
@ ^ [SY158: $i] : ( SV7 @ SY158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(263,plain,
! [SV9: $i] :
( ( ( in @ ( sK7_SY162 @ SV9 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(264,plain,
! [SV9: $i] :
( ( ( in @ ( sK7_SY162 @ SV9 ) @ SV9 )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ omega )
| ( in @ SY163 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(265,plain,
! [SV11: $i,SV20: $i] :
( ( ( in @ SV20 @ ( sK9_SY211 @ SV11 @ SV20 ) )
= $true )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(266,plain,
! [SV20: $i,SV11: $i] :
( ( ( in @ ( sK9_SY211 @ SV11 @ SV20 ) @ SV11 )
= $true )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(267,plain,
! [SV11: $i,SV33: $i,SV20: $i] :
( ( ( in @ SV20 @ SV33 )
= $false )
| ( ( ~ ( in @ SV33 @ SV11 ) )
= $true )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(268,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( ~ ( ~ ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV21 )
| ~ ( SV12 @ SY259 @ SV36 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(269,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ( ~ ~ ! [SY260: $i] :
~ ~ ( ~ ( in @ SY260 @ SV21 )
| ~ ( SV12 @ SY260 @ SV36 ) )
| ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(270,plain,
! [SV30: $i,SV21: $i,SV12: $i > $i > $o] :
( ( ( ! [SY248: $i] :
( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SY248 )
| ( SV30 = SY248 ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(271,plain,
! [SV13: $i] :
( ( ! [SY225: $i] :
( ~ ( in @ SY225 @ ( sK2_SY178 @ SV13 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SY225 )
| ( in @ SY180 @ SV13 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(272,plain,
! [SV13: $i] :
( ( ! [SY227: $i,SY228: $i] :
( ~ ~ ( ~ ( in @ SY227 @ SV13 )
| ~ ( in @ SY228 @ SV13 ) )
| ~ ! [SY229: $i] :
( ~ ( in @ SY229 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY227 @ SY229 )
| ( in @ SY228 @ SY229 ) )
| ~ ( ~ ( in @ SY228 @ SY229 )
| ( in @ SY227 @ SY229 ) ) ) )
| ( SY227 = SY228 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(273,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SV38 @ ( sK2_SY178 @ SV13 ) ) ) )
= $true )
| ( ( ! [SY264: $i] :
( ~ ( in @ SY264 @ SV37 )
| ( in @ SY264 @ SV38 ) )
| ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(274,plain,
! [SV13: $i,SV31: $i] :
( ( ( ! [SY249: $i] :
( ~ ( in @ SY249 @ SV31 )
| ( in @ SY249 @ SV13 ) ) )
= $false )
| ( ( ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(275,plain,
! [SV4: $i,SV27: $i] :
( ( ( ! [SY247: $i] :
~ ~ ( ~ ( in @ SY247 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SY247 @ SV4 ) ) )
= $true )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(276,plain,
! [SV9: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ omega )
| ( in @ SV39 @ SV9 ) )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( in @ ( sK7_SY162 @ SV9 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(277,plain,
! [SV9: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ omega )
| ( in @ SV40 @ SV9 ) )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( in @ ( sK7_SY162 @ SV9 ) @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(278,plain,
! [SV20: $i,SV11: $i,SV33: $i] :
( ( ( in @ SV33 @ SV11 )
= $false )
| ( ( in @ SV20 @ SV33 )
= $false )
| ( ( in @ SV20 @ ( setunion @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(279,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( ~ ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV21 )
| ~ ( SV12 @ SY259 @ SV36 ) ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(280,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY260: $i] :
~ ~ ( ~ ( in @ SY260 @ SV21 )
| ~ ( SV12 @ SY260 @ SV36 ) )
| ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(281,plain,
! [SV30: $i,SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
| ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[270]) ).
thf(282,plain,
! [SV13: $i,SV41: $i] :
( ( ~ ( in @ SV41 @ ( sK2_SY178 @ SV13 ) )
| ! [SY266: $i] :
( ~ ( in @ SY266 @ SV41 )
| ( in @ SY266 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(283,plain,
! [SV13: $i,SV42: $i] :
( ( ! [SY267: $i] :
( ~ ~ ( ~ ( in @ SV42 @ SV13 )
| ~ ( in @ SY267 @ SV13 ) )
| ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY268 )
| ( in @ SY267 @ SY268 ) )
| ~ ( ~ ( in @ SY267 @ SY268 )
| ( in @ SV42 @ SY268 ) ) ) )
| ( SV42 = SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(284,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( ~ ( ~ ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SV38 @ ( sK2_SY178 @ SV13 ) ) ) )
= $false )
| ( ( ! [SY264: $i] :
( ~ ( in @ SY264 @ SV37 )
| ( in @ SY264 @ SV38 ) )
| ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(285,plain,
! [SV31: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
| ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 ) )
= $false )
| ( ( ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[274]) ).
thf(286,plain,
! [SV4: $i,SV27: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ SV43 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SV43 @ SV4 ) ) )
= $true )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(287,plain,
! [SV9: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ omega ) )
= $true )
| ( ( in @ SV39 @ SV9 )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( in @ ( sK7_SY162 @ SV9 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(288,plain,
! [SV9: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ omega ) )
= $true )
| ( ( in @ SV40 @ SV9 )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( in @ ( sK7_SY162 @ SV9 ) @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(289,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( ~ ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV21 )
| ~ ( SV12 @ SY259 @ SV36 ) ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(290,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY260: $i] :
~ ~ ( ~ ( in @ SY260 @ SV21 )
| ~ ( SV12 @ SY260 @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(291,plain,
! [SV30: $i,SV21: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(292,plain,
! [SV12: $i > $i > $o,SV21: $i,SV30: $i] :
( ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(293,plain,
! [SV13: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ ( sK2_SY178 @ SV13 ) ) )
= $true )
| ( ( ! [SY266: $i] :
( ~ ( in @ SY266 @ SV41 )
| ( in @ SY266 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(294,plain,
! [SV44: $i,SV13: $i,SV42: $i] :
( ( ~ ~ ( ~ ( in @ SV42 @ SV13 )
| ~ ( in @ SV44 @ SV13 ) )
| ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY269 )
| ( in @ SV44 @ SY269 ) )
| ~ ( ~ ( in @ SV44 @ SY269 )
| ( in @ SV42 @ SY269 ) ) ) )
| ( SV42 = SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(295,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SV38 @ ( sK2_SY178 @ SV13 ) ) )
= $true )
| ( ( ! [SY264: $i] :
( ~ ( in @ SY264 @ SV37 )
| ( in @ SY264 @ SV38 ) )
| ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(296,plain,
! [SV31: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 ) )
= $false )
| ( ( ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(297,plain,
! [SV31: $i,SV13: $i] :
( ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(298,plain,
! [SV4: $i,SV27: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SV43 @ SV4 ) ) )
= $false )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(299,plain,
! [SV9: $i,SV39: $i] :
( ( ( in @ SV39 @ omega )
= $false )
| ( ( in @ SV39 @ SV9 )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( in @ ( sK7_SY162 @ SV9 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(300,plain,
! [SV9: $i,SV40: $i] :
( ( ( in @ SV40 @ omega )
= $false )
| ( ( in @ SV40 @ SV9 )
= $true )
| ( ( in @ emptyset @ SV9 )
= $false )
| ( ( in @ ( sK7_SY162 @ SV9 ) @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(301,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV21 )
| ~ ( SV12 @ SY259 @ SV36 ) ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(302,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ! [SY260: $i] :
~ ~ ( ~ ( in @ SY260 @ SV21 )
| ~ ( SV12 @ SY260 @ SV36 ) ) )
= $false )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(303,plain,
! [SV30: $i,SV21: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( ~ ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(304,plain,
! [SV30: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(305,plain,
! [SV13: $i,SV41: $i] :
( ( ( in @ SV41 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( ! [SY266: $i] :
( ~ ( in @ SY266 @ SV41 )
| ( in @ SY266 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(306,plain,
! [SV44: $i,SV13: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( in @ SV42 @ SV13 )
| ~ ( in @ SV44 @ SV13 ) ) )
= $true )
| ( ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY269 )
| ( in @ SV44 @ SY269 ) )
| ~ ( ~ ( in @ SV44 @ SY269 )
| ( in @ SV42 @ SY269 ) ) ) )
| ( SV42 = SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(307,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ ( sK2_SY178 @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV38 @ ( sK2_SY178 @ SV13 ) ) )
= $true )
| ( ( ! [SY264: $i] :
( ~ ( in @ SY264 @ SV37 )
| ( in @ SY264 @ SV38 ) )
| ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(308,plain,
! [SV31: $i,SV13: $i] :
( ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( ~ ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(309,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(310,plain,
! [SV4: $i,SV27: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( sK6_SY149 @ SV27 @ SV4 ) )
| ~ ( in @ SV43 @ SV4 ) )
= $true )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(311,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV21 )
| ~ ( SV12 @ SY259 @ SV36 ) ) )
= $false )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(312,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY260: $i] :
~ ~ ( ~ ( in @ SY260 @ SV21 )
| ~ ( SV12 @ SY260 @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(313,plain,
! [SV30: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY216: $i] :
~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY217 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY217 ) )
| ( in @ SY217 @ SY216 ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(314,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i] :
( ( ( ~ ! [SY270: $i] :
~ ( ~ ( ~ ( in @ SY270 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY270 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY270 ) )
| ( in @ SY270 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[304]) ).
thf(315,plain,
! [SV13: $i,SV41: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV41 )
| ( in @ SV45 @ SV13 ) )
= $true )
| ( ( in @ SV41 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(316,plain,
! [SV44: $i,SV13: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ SV42 @ SV13 )
| ~ ( in @ SV44 @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY269 )
| ( in @ SV44 @ SY269 ) )
| ~ ( ~ ( in @ SV44 @ SY269 )
| ( in @ SV42 @ SY269 ) ) ) )
| ( SV42 = SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(317,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV38 @ ( sK2_SY178 @ SV13 ) ) )
= $true )
| ( ( ! [SY264: $i] :
( ~ ( in @ SY264 @ SV37 )
| ( in @ SY264 @ SV38 ) )
| ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(318,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(319,plain,
! [SV13: $i,SV31: $i] :
( ( ( ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(320,plain,
! [SV4: $i,SV27: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( sK6_SY149 @ SV27 @ SV4 ) ) )
= $true )
| ( ( ~ ( in @ SV43 @ SV4 ) )
= $true )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(321,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV21 )
| ~ ( SV12 @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV36 ) ) )
= $false )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[311]) ).
thf(322,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( in @ SV46 @ SV21 )
| ~ ( SV12 @ SV46 @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(323,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i] :
( ( ( ~ ! [SY273: $i] :
~ ( ~ ( ~ ( in @ SY273 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY273 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY273 ) )
| ( in @ SY273 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[313]) ).
thf(324,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i] :
( ( ( ! [SY270: $i] :
~ ( ~ ( ~ ( in @ SY270 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY270 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY270 ) )
| ( in @ SY270 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) ) ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(325,plain,
! [SV13: $i,SV41: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV41 ) )
= $true )
| ( ( in @ SV45 @ SV13 )
= $true )
| ( ( in @ SV41 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(326,plain,
! [SV44: $i,SV13: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV13 )
| ~ ( in @ SV44 @ SV13 ) )
= $true )
| ( ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY269 )
| ( in @ SV44 @ SY269 ) )
| ~ ( ~ ( in @ SV44 @ SY269 )
| ( in @ SV42 @ SY269 ) ) ) )
| ( SV42 = SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(327,plain,
! [SV37: $i,SV13: $i,SV38: $i] :
( ( ( in @ SV38 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( ! [SY264: $i] :
( ~ ( in @ SY264 @ SV37 )
| ( in @ SY264 @ SV38 ) )
| ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(328,plain,
! [SV13: $i,SV31: $i] :
( ( ( ! [SY250: $i] :
~ ( in @ SY250 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(329,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(330,plain,
! [SV4: $i,SV27: $i,SV43: $i] :
( ( ( in @ SV43 @ ( sK6_SY149 @ SV27 @ SV4 ) )
= $false )
| ( ( ~ ( in @ SV43 @ SV4 ) )
= $true )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(331,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV21 )
| ~ ( SV12 @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(332,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i,SV46: $i] :
( ( ( ~ ( ~ ( in @ SV46 @ SV21 )
| ~ ( SV12 @ SV46 @ SV36 ) ) )
= $false )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(333,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i] :
( ( ( ! [SY273: $i] :
~ ( ~ ( ~ ( in @ SY273 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY218: $i] :
~ ~ ( ~ ( in @ SY218 @ SV21 )
| ~ ( SV12 @ SY218 @ SY273 ) ) )
| ~ ( ~ ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY219 @ SV21 )
| ~ ( SV12 @ SY219 @ SY273 ) )
| ( in @ SY273 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) ) ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(334,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV48: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY276: $i] :
~ ~ ( ~ ( in @ SY276 @ SV21 )
| ~ ( SV12 @ SY276 @ SV48 ) ) )
| ~ ( ~ ~ ! [SY277: $i] :
~ ~ ( ~ ( in @ SY277 @ SV21 )
| ~ ( SV12 @ SY277 @ SV48 ) )
| ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) ) ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(335,plain,
! [SV13: $i,SV41: $i,SV45: $i] :
( ( ( in @ SV45 @ SV41 )
= $false )
| ( ( in @ SV45 @ SV13 )
= $true )
| ( ( in @ SV41 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(336,plain,
! [SV44: $i,SV13: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV13 ) )
= $true )
| ( ( ~ ( in @ SV44 @ SV13 ) )
= $true )
| ( ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY269 )
| ( in @ SV44 @ SY269 ) )
| ~ ( ~ ( in @ SV44 @ SY269 )
| ( in @ SV42 @ SY269 ) ) ) )
| ( SV42 = SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(337,plain,
! [SV13: $i,SV38: $i,SV37: $i] :
( ( ( ! [SY264: $i] :
( ~ ( in @ SY264 @ SV37 )
| ( in @ SY264 @ SV38 ) ) )
= $true )
| ( ( ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(338,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(339,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( in @ SV47 @ SV31 )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(340,plain,
! [SV27: $i,SV4: $i,SV43: $i] :
( ( ( in @ SV43 @ SV4 )
= $false )
| ( ( in @ SV43 @ ( sK6_SY149 @ SV27 @ SV4 ) )
= $false )
| ( ( in @ SV27 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(341,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( ~ ( in @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV21 )
| ~ ( SV12 @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV36 ) )
= $false )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(342,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV21 )
| ~ ( SV12 @ SV46 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(343,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV50: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY278: $i] :
~ ~ ( ~ ( in @ SY278 @ SV21 )
| ~ ( SV12 @ SY278 @ SV50 ) ) )
| ~ ( ~ ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV21 )
| ~ ( SV12 @ SY279 @ SV50 ) )
| ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) ) ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(344,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV48: $i] :
( ( ( ~ ( ~ ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY276: $i] :
~ ~ ( ~ ( in @ SY276 @ SV21 )
| ~ ( SV12 @ SY276 @ SV48 ) ) )
| ~ ( ~ ~ ! [SY277: $i] :
~ ~ ( ~ ( in @ SY277 @ SV21 )
| ~ ( SV12 @ SY277 @ SV48 ) )
| ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(345,plain,
! [SV44: $i,SV13: $i,SV42: $i] :
( ( ( in @ SV42 @ SV13 )
= $false )
| ( ( ~ ( in @ SV44 @ SV13 ) )
= $true )
| ( ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY269 )
| ( in @ SV44 @ SY269 ) )
| ~ ( ~ ( in @ SV44 @ SY269 )
| ( in @ SV42 @ SY269 ) ) ) )
| ( SV42 = SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(346,plain,
! [SV13: $i,SV38: $i,SV37: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ SV37 )
| ( in @ SV51 @ SV38 ) )
= $true )
| ( ( ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(347,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( in @ SV49 @ SV31 )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( ~ ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(348,plain,
! [SV47: $i,SV31: $i,SV13: $i] :
( ( ( ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(349,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( ~ ( in @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV21 ) )
= $false )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(350,plain,
! [SV21: $i,SV36: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV36 ) )
= $false )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(351,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV21 ) )
= $true )
| ( ( ~ ( SV12 @ SV46 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(352,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV50: $i] :
( ( ( ~ ( ~ ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY278: $i] :
~ ~ ( ~ ( in @ SY278 @ SV21 )
| ~ ( SV12 @ SY278 @ SV50 ) ) )
| ~ ( ~ ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV21 )
| ~ ( SV12 @ SY279 @ SV50 ) )
| ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(353,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV48: $i] :
( ( ( ~ ( ~ ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY276: $i] :
~ ~ ( ~ ( in @ SY276 @ SV21 )
| ~ ( SV12 @ SY276 @ SV48 ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(354,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ( ~ ~ ! [SY277: $i] :
~ ~ ( ~ ( in @ SY277 @ SV21 )
| ~ ( SV12 @ SY277 @ SV48 ) )
| ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(355,plain,
! [SV42: $i,SV13: $i,SV44: $i] :
( ( ( in @ SV44 @ SV13 )
= $false )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY269 )
| ( in @ SV44 @ SY269 ) )
| ~ ( ~ ( in @ SV44 @ SY269 )
| ( in @ SV42 @ SY269 ) ) ) )
| ( SV42 = SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(356,plain,
! [SV13: $i,SV38: $i,SV37: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ SV37 ) )
= $true )
| ( ( in @ SV51 @ SV38 )
= $true )
| ( ( ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(357,plain,
! [SV49: $i,SV31: $i,SV13: $i] :
( ( ( ! [SY251: $i] :
~ ~ ! [SY252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY251 @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY252 @ SV31 ) )
| ~ ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( in @ SY253 @ SY251 )
| ~ ( in @ SY253 @ SV31 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY178 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY240 )
| ( in @ SX6 @ SY251 ) )
| ( in @ SY252 @ SY240 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(358,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ~ ! [SY280: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY280 @ SV31 ) )
| ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
| ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK2_SY178 @ SV13 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ SY280 @ SY282 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[348]) ).
thf(359,plain,
! [SV21: $i,SV12: $i > $i > $o,SV36: $i] :
( ( ( in @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV21 )
= $true )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(360,plain,
! [SV21: $i,SV36: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK16_SY259 @ SV36 @ SV12 @ SV21 ) @ SV36 )
= $true )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $false )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(361,plain,
! [SV36: $i,SV12: $i > $i > $o,SV21: $i,SV46: $i] :
( ( ( in @ SV46 @ SV21 )
= $false )
| ( ( ~ ( SV12 @ SV46 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(362,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV50: $i] :
( ( ( ~ ( ~ ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY278: $i] :
~ ~ ( ~ ( in @ SY278 @ SV21 )
| ~ ( SV12 @ SY278 @ SV50 ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(363,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ( ~ ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV21 )
| ~ ( SV12 @ SY279 @ SV50 ) )
| ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) ) ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(364,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY276: $i] :
~ ~ ( ~ ( in @ SY276 @ SV21 )
| ~ ( SV12 @ SY276 @ SV48 ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(365,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY277: $i] :
~ ~ ( ~ ( in @ SY277 @ SV21 )
| ~ ( SV12 @ SY277 @ SV48 ) )
| ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(366,plain,
! [SV44: $i,SV42: $i,SV13: $i] :
( ( ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY269 )
| ( in @ SV44 @ SY269 ) )
| ~ ( ~ ( in @ SV44 @ SY269 )
| ( in @ SV42 @ SY269 ) ) ) ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(367,plain,
! [SV13: $i,SV38: $i,SV37: $i,SV51: $i] :
( ( ( in @ SV51 @ SV37 )
= $false )
| ( ( in @ SV51 @ SV38 )
= $true )
| ( ( ! [SY265: $i] :
( ~ ( in @ SY265 @ SV38 )
| ( in @ SY265 @ SV37 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(368,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ~ ! [SY284: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY284 @ SV31 ) )
| ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
| ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK2_SY178 @ SV13 ) )
| ! [SY287: $i] :
( ~ ( in @ SY287 @ SY286 )
| ( in @ SY287 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ SY284 @ SY286 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[357]) ).
thf(369,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ! [SY280: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY280 @ SV31 ) )
| ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
| ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK2_SY178 @ SV13 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ SY280 @ SY282 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(370,plain,
! [SV21: $i,SV36: $i,SV46: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ SV46 @ SV36 )
= $false )
| ( ( in @ SV46 @ SV21 )
= $false )
| ( ( in @ SV36 @ ( sK10_SY216 @ SV12 @ SV21 ) )
= $true )
| ( ( in @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(371,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
| ~ ! [SY278: $i] :
~ ~ ( ~ ( in @ SY278 @ SV21 )
| ~ ( SV12 @ SY278 @ SV50 ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(372,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV21 )
| ~ ( SV12 @ SY279 @ SV50 ) )
| ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(373,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) ) )
= $true )
| ( ( ~ ! [SY276: $i] :
~ ~ ( ~ ( in @ SY276 @ SV21 )
| ~ ( SV12 @ SY276 @ SV48 ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(374,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY277: $i] :
~ ~ ( ~ ( in @ SY277 @ SV21 )
| ~ ( SV12 @ SY277 @ SV48 ) ) )
= $true )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(375,plain,
! [SV44: $i,SV42: $i,SV13: $i] :
( ( ( ! [SY269: $i] :
( ~ ( in @ SY269 @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ SY269 )
| ( in @ SV44 @ SY269 ) )
| ~ ( ~ ( in @ SV44 @ SY269 )
| ( in @ SV42 @ SY269 ) ) ) ) )
= $false )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(376,plain,
! [SV13: $i,SV51: $i,SV37: $i,SV38: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV38 )
| ( in @ SV52 @ SV37 ) )
= $true )
| ( ( in @ SV51 @ SV38 )
= $true )
| ( ( in @ SV51 @ SV37 )
= $false )
| ( ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(377,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ! [SY284: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY284 @ SV31 ) )
| ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
| ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK2_SY178 @ SV13 ) )
| ! [SY287: $i] :
( ~ ( in @ SY287 @ SY286 )
| ( in @ SY287 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ SY284 @ SY286 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(378,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ! [SY280: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY280 @ SV31 ) )
| ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
| ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK2_SY178 @ SV13 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ SY280 @ SY282 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(379,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) ) )
= $true )
| ( ( ~ ! [SY278: $i] :
~ ~ ( ~ ( in @ SY278 @ SV21 )
| ~ ( SV12 @ SY278 @ SV50 ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(380,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV21 )
| ~ ( SV12 @ SY279 @ SV50 ) ) )
= $true )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(381,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV48: $i] :
( ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( ~ ! [SY276: $i] :
~ ~ ( ~ ( in @ SY276 @ SV21 )
| ~ ( SV12 @ SY276 @ SV48 ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(382,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ! [SY277: $i] :
~ ~ ( ~ ( in @ SY277 @ SV21 )
| ~ ( SV12 @ SY277 @ SV48 ) ) )
= $false )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(383,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( ~ ( in @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) )
| ~ ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) ) ) )
= $false )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[375]) ).
thf(384,plain,
! [SV13: $i,SV51: $i,SV37: $i,SV38: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV38 ) )
= $true )
| ( ( in @ SV52 @ SV37 )
= $true )
| ( ( in @ SV51 @ SV38 )
= $true )
| ( ( in @ SV51 @ SV37 )
= $false )
| ( ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(385,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ! [SY284: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ SY284 @ SV31 ) )
| ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
| ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK2_SY178 @ SV13 ) )
| ! [SY287: $i] :
( ~ ( in @ SY287 @ SY286 )
| ( in @ SY287 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ SY284 @ SY286 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(386,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) )
| ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
| ~ ! [SY289: $i] :
( ~ ( in @ SY289 @ ( sK2_SY178 @ SV13 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY289 )
| ( in @ SY283 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SY289 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[378]) ).
thf(387,plain,
! [SV21: $i,SV12: $i > $i > $o,SV30: $i,SV50: $i] :
( ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( ~ ! [SY278: $i] :
~ ~ ( ~ ( in @ SY278 @ SV21 )
| ~ ( SV12 @ SY278 @ SV50 ) ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(388,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV21 )
| ~ ( SV12 @ SY279 @ SV50 ) ) )
= $false )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(389,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY276: $i] :
~ ~ ( ~ ( in @ SY276 @ SV21 )
| ~ ( SV12 @ SY276 @ SV48 ) ) )
= $false )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(390,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY277: $i] :
~ ~ ( ~ ( in @ SY277 @ SV21 )
| ~ ( SV12 @ SY277 @ SV48 ) ) )
= $true )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(391,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( ~ ( in @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) @ ( sK2_SY178 @ SV13 ) ) )
= $false )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(392,plain,
! [SV13: $i,SV44: $i,SV42: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) )
| ~ ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) ) ) )
= $false )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(393,plain,
! [SV13: $i,SV51: $i,SV37: $i,SV38: $i,SV52: $i] :
( ( ( in @ SV52 @ SV38 )
= $false )
| ( ( in @ SV52 @ SV37 )
= $true )
| ( ( in @ SV51 @ SV38 )
= $true )
| ( ( in @ SV51 @ SV37 )
= $false )
| ( ( in @ SV37 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK2_SY178 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(394,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) )
| ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
| ~ ! [SY292: $i] :
( ~ ( in @ SY292 @ ( sK2_SY178 @ SV13 ) )
| ! [SY287: $i] :
( ~ ( in @ SY287 @ SY292 )
| ( in @ SY287 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SY292 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[385]) ).
thf(395,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) )
| ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
| ~ ! [SY289: $i] :
( ~ ( in @ SY289 @ ( sK2_SY178 @ SV13 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY289 )
| ( in @ SY283 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SY289 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(396,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY278: $i] :
~ ~ ( ~ ( in @ SY278 @ SV21 )
| ~ ( SV12 @ SY278 @ SV50 ) ) )
= $false )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(397,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i] :
( ( ( ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV21 )
| ~ ( SV12 @ SY279 @ SV50 ) ) )
= $true )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(398,plain,
! [SV21: $i,SV12: $i > $i > $o,SV48: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV21 )
| ~ ( SV12 @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV48 ) ) )
= $false )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[389]) ).
thf(399,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( in @ SV53 @ SV21 )
| ~ ( SV12 @ SV53 @ SV48 ) ) )
= $true )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(400,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( in @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(401,plain,
! [SV13: $i,SV44: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) )
| ~ ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(402,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) )
| ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
| ~ ! [SY292: $i] :
( ~ ( in @ SY292 @ ( sK2_SY178 @ SV13 ) )
| ! [SY287: $i] :
( ~ ( in @ SY287 @ SY292 )
| ( in @ SY287 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SY292 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(403,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) )
| ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
| ~ ! [SY289: $i] :
( ~ ( in @ SY289 @ ( sK2_SY178 @ SV13 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY289 )
| ( in @ SY283 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SY289 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(404,plain,
! [SV21: $i,SV12: $i > $i > $o,SV50: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV21 )
| ~ ( SV12 @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV50 ) ) )
= $false )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[396]) ).
thf(405,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ( in @ SV54 @ SV21 )
| ~ ( SV12 @ SV54 @ SV50 ) ) )
= $true )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(406,plain,
! [SV21: $i,SV12: $i > $i > $o,SV48: $i,SV30: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV21 )
| ~ ( SV12 @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV48 ) ) )
= $true )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(407,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( ~ ( ~ ( in @ SV53 @ SV21 )
| ~ ( SV12 @ SV53 @ SV48 ) ) )
= $false )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(408,plain,
! [SV13: $i,SV44: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(409,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) )
| ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
| ~ ! [SY292: $i] :
( ~ ( in @ SY292 @ ( sK2_SY178 @ SV13 ) )
| ! [SY287: $i] :
( ~ ( in @ SY287 @ SY292 )
| ( in @ SY287 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SY292 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(410,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) )
| ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(411,plain,
! [SV31: $i,SV47: $i,SV13: $i] :
( ( ( ~ ! [SY289: $i] :
( ~ ( in @ SY289 @ ( sK2_SY178 @ SV13 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY289 )
| ( in @ SY283 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SY289 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(412,plain,
! [SV21: $i,SV12: $i > $i > $o,SV50: $i,SV30: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV21 )
| ~ ( SV12 @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV50 ) ) )
= $true )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(413,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i,SV54: $i] :
( ( ( ~ ( ~ ( in @ SV54 @ SV21 )
| ~ ( SV12 @ SV54 @ SV50 ) ) )
= $false )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(414,plain,
! [SV21: $i,SV12: $i > $i > $o,SV48: $i,SV30: $i] :
( ( ( ~ ( in @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV21 )
| ~ ( SV12 @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV48 ) )
= $false )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(415,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV21 )
| ~ ( SV12 @ SV53 @ SV48 ) )
= $true )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(416,plain,
! [SV13: $i,SV44: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(417,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) )
| ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(418,plain,
! [SV31: $i,SV49: $i,SV13: $i] :
( ( ( ~ ! [SY292: $i] :
( ~ ( in @ SY292 @ ( sK2_SY178 @ SV13 ) )
| ! [SY287: $i] :
( ~ ( in @ SY287 @ SY292 )
| ( in @ SY287 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SY292 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(419,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) )
| ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(420,plain,
! [SV31: $i,SV47: $i,SV13: $i] :
( ( ( ! [SY289: $i] :
( ~ ( in @ SY289 @ ( sK2_SY178 @ SV13 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY289 )
| ( in @ SY283 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SY289 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(421,plain,
! [SV21: $i,SV12: $i > $i > $o,SV50: $i,SV30: $i] :
( ( ( ~ ( in @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV21 )
| ~ ( SV12 @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV50 ) )
= $false )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(422,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV21 )
| ~ ( SV12 @ SV54 @ SV50 ) )
= $true )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(423,plain,
! [SV21: $i,SV12: $i > $i > $o,SV48: $i,SV30: $i] :
( ( ( ~ ( in @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV21 ) )
= $false )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(424,plain,
! [SV21: $i,SV48: $i,SV30: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV48 ) )
= $false )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(425,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV21 ) )
= $true )
| ( ( ~ ( SV12 @ SV53 @ SV48 ) )
= $true )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(426,plain,
! [SV13: $i,SV44: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(427,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(428,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) )
| ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(429,plain,
! [SV31: $i,SV49: $i,SV13: $i] :
( ( ( ! [SY292: $i] :
( ~ ( in @ SY292 @ ( sK2_SY178 @ SV13 ) )
| ! [SY287: $i] :
( ~ ( in @ SY287 @ SY292 )
| ( in @ SY287 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SY292 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(430,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) )
| ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(431,plain,
! [SV31: $i,SV47: $i,SV13: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( sK2_SY178 @ SV13 ) )
| ! [SY294: $i] :
( ~ ( in @ SY294 @ SV55 )
| ( in @ SY294 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV55 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(432,plain,
! [SV21: $i,SV12: $i > $i > $o,SV50: $i,SV30: $i] :
( ( ( ~ ( in @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV21 ) )
= $false )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(433,plain,
! [SV21: $i,SV50: $i,SV30: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV50 ) )
= $false )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(434,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV21 ) )
= $true )
| ( ( ~ ( SV12 @ SV54 @ SV50 ) )
= $true )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(435,plain,
! [SV21: $i,SV12: $i > $i > $o,SV48: $i,SV30: $i] :
( ( ( in @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV21 )
= $true )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(436,plain,
! [SV21: $i,SV48: $i,SV30: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK23_SY276 @ SV30 @ SV48 @ SV12 @ SV21 ) @ SV48 )
= $true )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(437,plain,
! [SV30: $i,SV48: $i,SV12: $i > $i > $o,SV21: $i,SV53: $i] :
( ( ( in @ SV53 @ SV21 )
= $false )
| ( ( ~ ( SV12 @ SV53 @ SV48 ) )
= $true )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(438,plain,
! [SV13: $i,SV44: $i,SV42: $i] :
( ( ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(439,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) )
= $false )
| ( ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $false )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(440,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) )
| ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(441,plain,
! [SV31: $i,SV49: $i,SV13: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ ( sK2_SY178 @ SV13 ) )
| ! [SY295: $i] :
( ~ ( in @ SY295 @ SV56 )
| ( in @ SY295 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV56 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(442,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(443,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(444,plain,
! [SV31: $i,SV47: $i,SV13: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( sK2_SY178 @ SV13 ) ) )
= $true )
| ( ( ! [SY294: $i] :
( ~ ( in @ SY294 @ SV55 )
| ( in @ SY294 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV55 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(445,plain,
! [SV21: $i,SV12: $i > $i > $o,SV50: $i,SV30: $i] :
( ( ( in @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV21 )
= $true )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(446,plain,
! [SV21: $i,SV50: $i,SV30: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK24_SY278 @ SV30 @ SV50 @ SV12 @ SV21 ) @ SV50 )
= $true )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(447,plain,
! [SV30: $i,SV50: $i,SV12: $i > $i > $o,SV21: $i,SV54: $i] :
( ( ( in @ SV54 @ SV21 )
= $false )
| ( ( ~ ( SV12 @ SV54 @ SV50 ) )
= $true )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(448,plain,
! [SV30: $i,SV21: $i,SV48: $i,SV53: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ SV53 @ SV48 )
= $false )
| ( ( in @ SV53 @ SV21 )
= $false )
| ( ( in @ SV48 @ ( sK15_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV30
= ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(449,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
| ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) )
= $false )
| ( ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(450,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) )
= $false )
| ( ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $false )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(451,plain,
! [SV13: $i,SV44: $i,SV42: $i] :
( ( ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $false )
| ( ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $false )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(452,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(453,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(454,plain,
! [SV31: $i,SV49: $i,SV13: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ ( sK2_SY178 @ SV13 ) ) )
= $true )
| ( ( ! [SY295: $i] :
( ~ ( in @ SY295 @ SV56 )
| ( in @ SY295 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV56 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(455,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(456,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(457,plain,
! [SV31: $i,SV47: $i,SV13: $i,SV55: $i] :
( ( ( in @ SV55 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( ! [SY294: $i] :
( ~ ( in @ SY294 @ SV55 )
| ( in @ SY294 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
| ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV55 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(458,plain,
! [SV30: $i,SV21: $i,SV50: $i,SV54: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ SV54 @ SV50 )
= $false )
| ( ( in @ SV54 @ SV21 )
= $false )
| ( ( in @ SV50 @ ( sK17_SY216 @ SV30 @ SV12 @ SV21 ) )
= $true )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ SV30 )
= $false )
| ( ( SV12 @ ( sK4_SY213 @ SV12 @ SV21 ) @ ( sK13_SY248 @ SV30 @ SV21 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(459,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) ) )
= $false )
| ( ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(460,plain,
! [SV13: $i,SV44: $i,SV42: $i] :
( ( ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $false )
| ( ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(461,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $true )
| ( ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $false )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(462,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(463,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(464,plain,
! [SV31: $i,SV49: $i,SV13: $i,SV56: $i] :
( ( ( in @ SV56 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( ! [SY295: $i] :
( ~ ( in @ SY295 @ SV56 )
| ( in @ SY295 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
| ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV56 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(465,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(466,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(467,plain,
! [SV13: $i,SV31: $i,SV47: $i,SV55: $i] :
( ( ( ! [SY294: $i] :
( ~ ( in @ SY294 @ SV55 )
| ( in @ SY294 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) ) )
= $true )
| ( ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV55 )
= $true )
| ( ( in @ SV55 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(468,plain,
! [SV13: $i,SV42: $i,SV44: $i] :
( ( ( in @ SV44 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $true )
| ( ( in @ SV42 @ ( sK20_SY269 @ SV44 @ SV42 @ SV13 ) )
= $true )
| ( ( SV42 = SV44 )
= $true )
| ( ( in @ SV42 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(469,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
| ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(470,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(471,plain,
! [SV13: $i,SV31: $i,SV49: $i,SV56: $i] :
( ( ( ! [SY295: $i] :
( ~ ( in @ SY295 @ SV56 )
| ( in @ SY295 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) ) )
= $true )
| ( ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV56 )
= $true )
| ( ( in @ SV56 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(472,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(473,plain,
! [SV47: $i,SV31: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(474,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( ! [SY281: $i] :
~ ~ ( ~ ( in @ SY281 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SY281 @ SV31 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(475,plain,
! [SV13: $i,SV31: $i,SV47: $i,SV55: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV55 )
| ( in @ SV57 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
= $true )
| ( ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV55 )
= $true )
| ( ( in @ SV55 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(476,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(477,plain,
! [SV49: $i,SV31: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(478,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( ! [SY285: $i] :
~ ~ ( ~ ( in @ SY285 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SY285 @ SV31 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(479,plain,
! [SV13: $i,SV31: $i,SV49: $i,SV56: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ SV56 )
| ( in @ SV58 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
= $true )
| ( ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV56 )
= $true )
| ( ( in @ SV56 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(480,plain,
! [SV13: $i,SV31: $i,SV47: $i] :
( ( ( in @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(481,plain,
! [SV47: $i,SV31: $i,SV13: $i] :
( ( ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV31 )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(482,plain,
! [SV13: $i,SV31: $i,SV47: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( in @ SV59 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SV59 @ SV31 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(483,plain,
! [SV13: $i,SV31: $i,SV47: $i,SV55: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV55 ) )
= $true )
| ( ( in @ SV57 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
= $true )
| ( ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV55 )
= $true )
| ( ( in @ SV55 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(484,plain,
! [SV13: $i,SV31: $i,SV49: $i] :
( ( ( in @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) @ ( sK2_SY178 @ SV13 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(485,plain,
! [SV49: $i,SV31: $i,SV13: $i] :
( ( ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV31 )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(486,plain,
! [SV13: $i,SV31: $i,SV49: $i,SV60: $i] :
( ( ( ~ ~ ( ~ ( in @ SV60 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SV60 @ SV31 ) ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(487,plain,
! [SV13: $i,SV31: $i,SV49: $i,SV56: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ SV56 ) )
= $true )
| ( ( in @ SV58 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
= $true )
| ( ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV56 )
= $true )
| ( ( in @ SV56 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(488,plain,
! [SV13: $i,SV31: $i,SV47: $i,SV59: $i] :
( ( ( ~ ( ~ ( in @ SV59 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SV59 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(489,plain,
! [SV13: $i,SV31: $i,SV47: $i,SV55: $i,SV57: $i] :
( ( ( in @ SV57 @ SV55 )
= $false )
| ( ( in @ SV57 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
= $true )
| ( ( in @ ( sK21_SY280 @ SV13 @ SV31 @ SV47 ) @ SV55 )
= $true )
| ( ( in @ SV55 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(490,plain,
! [SV13: $i,SV31: $i,SV49: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ SV60 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SV60 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(491,plain,
! [SV13: $i,SV31: $i,SV49: $i,SV56: $i,SV58: $i] :
( ( ( in @ SV58 @ SV56 )
= $false )
| ( ( in @ SV58 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
= $true )
| ( ( in @ ( sK22_SY284 @ SV13 @ SV31 @ SV49 ) @ SV56 )
= $true )
| ( ( in @ SV56 @ ( sK2_SY178 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(492,plain,
! [SV13: $i,SV31: $i,SV47: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
| ~ ( in @ SV59 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(493,plain,
! [SV13: $i,SV31: $i,SV49: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
| ~ ( in @ SV60 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(494,plain,
! [SV13: $i,SV31: $i,SV47: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV59 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(495,plain,
! [SV13: $i,SV31: $i,SV49: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV60 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(496,plain,
! [SV13: $i,SV31: $i,SV47: $i,SV59: $i] :
( ( ( in @ SV59 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV59 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(497,plain,
! [SV13: $i,SV31: $i,SV49: $i,SV60: $i] :
( ( ( in @ SV60 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV60 @ SV31 ) )
= $true )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(498,plain,
! [SV13: $i,SV47: $i,SV31: $i,SV59: $i] :
( ( ( in @ SV59 @ SV31 )
= $false )
| ( ( in @ SV59 @ ( sK18_SY251 @ SV47 @ SV31 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(499,plain,
! [SV13: $i,SV49: $i,SV31: $i,SV60: $i] :
( ( ( in @ SV60 @ SV31 )
= $false )
| ( ( in @ SV60 @ ( sK19_SY251 @ SV49 @ SV31 @ SV13 ) )
= $false )
| ( ( in @ ( sK14_SY249 @ SV13 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV49 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(500,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,499,498,491,489,485,484,481,480,468,461,460,458,451,448,446,445,436,435,400,393,370,360,359,340,335,300,299,278,266,265,262,261,260,258,248,245,243,239,238,237,221,218,217,204,200,187,186,185,153,122,118,81,66]) ).
thf(501,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU499^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:25:36 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.80/0.61
% 1.80/0.61 No.of.Axioms: 0
% 1.80/0.61
% 1.80/0.61 Length.of.Defs: 3774
% 1.80/0.61
% 1.80/0.61 Contains.Choice.Funs: true
% 1.80/0.61 ...................
% 1.80/0.61
% 1.80/0.61 ********************************
% 1.80/0.61 * All subproblems solved! *
% 1.80/0.61 ********************************
% 1.80/0.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,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:500,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.80/0.61
% 1.80/0.61 %**** Beginning of derivation protocol ****
% 1.80/0.61 % SZS output start CNFRefutation
% See solution above
% 1.80/0.61
% 1.80/0.61 %**** End of derivation protocol ****
% 1.80/0.61 %**** no. of clauses in derivation: 501 ****
% 1.80/0.61 %**** clause counter: 500 ****
% 1.80/0.61
% 1.80/0.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,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:500,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------