%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU501^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 10:44:37 AM UTC 2026
% Result : Theorem 0.62s 0.35s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 20
% Syntax : Number of formulae : 481 ( 173 unt; 0 typ; 19 def)
% Number of atoms : 4286 (1305 equ; 0 cnn)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 10836 (1808 ~;1673 |; 112 &;7075 @)
% ( 18 <=>; 150 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 247 ( 247 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 23 con; 0-3 aty)
% Number of variables : 1823 ( 72 ^;1708 !; 43 ?;1823 :)
% 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_exuE1,type,
exuE1: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK10_SY158,type,
sK10_SY158: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_B,type,
sK12_B: $i > $i ).
thf(tp_sK13_SY176,type,
sK13_SY176: $i > $i > $i > $i ).
thf(tp_sK14_SY163,type,
sK14_SY163: $i > $i > $i ).
thf(tp_sK15_SY177,type,
sK15_SY177: $i > $i > $i ).
thf(tp_sK16_Xx,type,
sK16_Xx: $i > $i > $i ).
thf(tp_sK17_SY54,type,
sK17_SY54: $i > ( $i > $o ) > $i ).
thf(tp_sK18_Xx,type,
sK18_Xx: ( $i > $o ) > $i ).
thf(tp_sK19_SY71,type,
sK19_SY71: $i > ( $i > $o ) > $i ).
thf(tp_sK1_Xphi,type,
sK1_Xphi: $o ).
thf(tp_sK2_Xx,type,
sK2_Xx: $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: $i > $i > $i ).
thf(tp_sK4_Xx,type,
sK4_Xx: $i > $i > $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i > $i ).
thf(tp_sK6_Xx,type,
sK6_Xx: $i > $i ).
thf(tp_sK7_B,type,
sK7_B: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK8_Xy,type,
sK8_Xy: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK9_SY21,type,
sK9_SY21: $i > ( $i > $i > $o ) > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(prop2set,definition,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(2,negated_conjecture,
( ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY19: $i > $i > $o,SY20: $i] :
( ! [SY21: $i] :
( ( in @ SY21 @ SY20 )
=> ? [SY23: $i] :
( ( SY19 @ SY21 @ SY23 )
& ! [SY24: $i] :
( ( SY19 @ SY21 @ SY24 )
=> ( SY23 = SY24 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY20 )
& ( SY19 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) )
=> ( ! [SY51: $i > $o] :
( ? [SY53: $i] :
( ( SY51 @ SY53 )
& ! [SY54: $i] :
( ( SY51 @ SY54 )
=> ( SY53 = SY54 ) ) )
=> ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY68: $i > $o] :
( ? [SY70: $i] :
( ( SY68 @ SY70 )
& ! [SY71: $i] :
( ( SY68 @ SY71 )
=> ( SY70 = SY71 ) ) )
=> ? [Xx: $i] :
( ( SY68 @ Xx )
& ! [Xy: $i] :
( ( SY68 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY74: $o,SY75: $i] :
( ( in @ SY75
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY76: $i] : SY74 ) )
=> SY74 )
=> ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [SY19: $i > $i > $o,SY20: $i] :
( ! [SY21: $i] :
( ( in @ SY21 @ SY20 )
=> ? [SY23: $i] :
( ( SY19 @ SY21 @ SY23 )
& ! [SY24: $i] :
( ( SY19 @ SY21 @ SY24 )
=> ( SY23 = SY24 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY20 )
& ( SY19 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY51: $i > $o] :
( ? [SY53: $i] :
( ( SY51 @ SY53 )
& ! [SY54: $i] :
( ( SY51 @ SY54 )
=> ( SY53 = SY54 ) ) )
=> ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY68: $i > $o] :
( ? [SY70: $i] :
( ( SY68 @ SY70 )
& ! [SY71: $i] :
( ( SY68 @ SY71 )
=> ( SY70 = SY71 ) ) )
=> ? [Xx: $i] :
( ( SY68 @ Xx )
& ! [Xy: $i] :
( ( SY68 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [SY74: $o,SY75: $i] :
( ( in @ SY75
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY76: $i] : SY74 ) )
=> SY74 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ~ ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(23,plain,
( ( ( in @ sK2_Xx @ emptyset )
& ~ sK1_Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK3_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK3_Xx @ B @ A ) @ A )
| ( in @ ( sK3_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(25,plain,
( ( ! [Xx: $i] :
( ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) )
& ! [A: $i,Xy: $i] :
( ( Xy != Xx )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
& ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK4_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK4_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(27,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK5_B @ Xx @ A ) )
& ( in @ ( sK5_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(28,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK6_Xx @ A ) @ omega )
& ( in @ ( sK6_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK6_Xx @ A ) @ ( sK6_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(30,plain,
( ( ! [SY19: $i > $i > $o,SY20: $i] :
( ( ( in @ ( sK9_SY21 @ SY20 @ SY19 ) @ SY20 )
& ! [SY157: $i] :
( ( ( SY19 @ ( sK9_SY21 @ SY20 @ SY19 ) @ ( sK10_SY158 @ SY157 @ SY20 @ SY19 ) )
& ( SY157
!= ( sK10_SY158 @ SY157 @ SY20 @ SY19 ) ) )
| ~ ( SY19 @ ( sK9_SY21 @ SY20 @ SY19 ) @ SY157 ) ) )
| ( ! [SY153: $i] :
( ! [Xy: $i] :
( ~ ( SY19 @ Xy @ SY153 )
| ~ ( in @ Xy @ SY20 ) )
| ( in @ SY153 @ ( sK7_B @ SY20 @ SY19 ) ) )
& ! [SY155: $i] :
( ~ ( in @ SY155 @ ( sK7_B @ SY20 @ SY19 ) )
| ( ( SY19 @ ( sK8_Xy @ SY155 @ SY20 @ SY19 ) @ SY155 )
& ( in @ ( sK8_Xy @ SY155 @ SY20 @ SY19 ) @ SY20 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(31,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK11_B @ A ) @ A )
& ! [SY159: $i] :
( ~ ( in @ SY159 @ ( sK11_B @ A ) )
| ~ ( in @ SY159 @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(32,plain,
( ( ! [A: $i] :
( ! [SY160: $i] :
( ( ( in @ ( sK16_Xx @ SY160 @ A ) @ SY160 )
& ~ ( in @ ( sK16_Xx @ SY160 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY160 )
| ( ! [SY181: $i] :
( ~ ( in @ SY181 @ ( sK12_B @ A ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY181 )
| ( in @ SY179 @ ( sK14_SY163 @ SY160 @ A ) ) )
| ( in @ ( sK15_SY177 @ SY160 @ A ) @ SY181 ) )
& ( in @ ( sK14_SY163 @ SY160 @ A ) @ ( sK12_B @ A ) )
& ( in @ ( sK15_SY177 @ SY160 @ A ) @ SY160 )
& ! [SY180: $i] :
( ~ ( in @ SY180 @ ( sK14_SY163 @ SY160 @ A ) )
| ~ ( in @ SY180 @ SY160 ) ) ) )
& ! [SY168: $i,SY169: $i] :
( ~ ( in @ SY168 @ ( sK12_B @ A ) )
| ~ ( in @ SY169 @ ( sK12_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY168 )
| ( in @ Xx @ SY169 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY169 )
| ( in @ Xx @ SY168 ) ) )
& ! [SY172: $i] :
( ~ ( in @ SY172 @ ( sK12_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY172 )
| ( in @ Xx @ A ) ) )
& ! [SY174: $i,SY175: $i] :
( ~ ( in @ SY174 @ A )
| ~ ( in @ SY175 @ A )
| ( ( in @ ( sK13_SY176 @ SY175 @ SY174 @ A ) @ ( sK12_B @ A ) )
& ( ~ ( in @ SY174 @ ( sK13_SY176 @ SY175 @ SY174 @ A ) )
| ~ ( in @ SY175 @ ( sK13_SY176 @ SY175 @ SY174 @ A ) ) )
& ( ( in @ SY174 @ ( sK13_SY176 @ SY175 @ SY174 @ A ) )
| ( in @ SY175 @ ( sK13_SY176 @ SY175 @ SY174 @ A ) ) ) )
| ( SY174 = SY175 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(33,plain,
( ( ! [SY51: $i > $o] :
( ! [SY53: $i] :
( ( ( SY51 @ ( sK17_SY54 @ SY53 @ SY51 ) )
& ( SY53
!= ( sK17_SY54 @ SY53 @ SY51 ) ) )
| ~ ( SY51 @ SY53 ) )
| ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(34,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(35,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(36,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(37,plain,
( ( ! [SY68: $i > $o] :
( ! [SY70: $i] :
( ( ( SY68 @ ( sK19_SY71 @ SY70 @ SY68 ) )
& ( SY70
!= ( sK19_SY71 @ SY70 @ SY68 ) ) )
| ~ ( SY68 @ SY70 ) )
| ( ! [SY184: $i] :
( ~ ( SY68 @ SY184 )
| ( ( sK18_Xx @ SY68 )
= SY184 ) )
& ( SY68 @ ( sK18_Xx @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(38,plain,
( ( ! [SY74: $o] :
( ! [SY75: $i] :
~ ( in @ SY75
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY76: $i] : SY74 ) )
| SY74 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(39,plain,
( ( ! [SY74: $o] :
( ! [SY75: $i] :
~ ( in @ SY75
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY76: $i] : SY74 ) )
| SY74 ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [SY68: $i > $o] :
( ! [SY70: $i] :
( ( ( SY68 @ ( sK19_SY71 @ SY70 @ SY68 ) )
& ( SY70
!= ( sK19_SY71 @ SY70 @ SY68 ) ) )
| ~ ( SY68 @ SY70 ) )
| ( ! [SY184: $i] :
( ~ ( SY68 @ SY184 )
| ( ( sK18_Xx @ SY68 )
= SY184 ) )
& ( SY68 @ ( sK18_Xx @ SY68 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(41,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(42,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(43,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)],[34]) ).
thf(44,plain,
( ( ! [SY51: $i > $o] :
( ! [SY53: $i] :
( ( ( SY51 @ ( sK17_SY54 @ SY53 @ SY51 ) )
& ( SY53
!= ( sK17_SY54 @ SY53 @ SY51 ) ) )
| ~ ( SY51 @ SY53 ) )
| ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(45,plain,
( ( ! [A: $i] :
( ! [SY160: $i] :
( ( ( in @ ( sK16_Xx @ SY160 @ A ) @ SY160 )
& ~ ( in @ ( sK16_Xx @ SY160 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY160 )
| ( ! [SY181: $i] :
( ~ ( in @ SY181 @ ( sK12_B @ A ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SY181 )
| ( in @ SY179 @ ( sK14_SY163 @ SY160 @ A ) ) )
| ( in @ ( sK15_SY177 @ SY160 @ A ) @ SY181 ) )
& ( in @ ( sK14_SY163 @ SY160 @ A ) @ ( sK12_B @ A ) )
& ( in @ ( sK15_SY177 @ SY160 @ A ) @ SY160 )
& ! [SY180: $i] :
( ~ ( in @ SY180 @ ( sK14_SY163 @ SY160 @ A ) )
| ~ ( in @ SY180 @ SY160 ) ) ) )
& ! [SY168: $i,SY169: $i] :
( ~ ( in @ SY168 @ ( sK12_B @ A ) )
| ~ ( in @ SY169 @ ( sK12_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY168 )
| ( in @ Xx @ SY169 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY169 )
| ( in @ Xx @ SY168 ) ) )
& ! [SY172: $i] :
( ~ ( in @ SY172 @ ( sK12_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY172 )
| ( in @ Xx @ A ) ) )
& ! [SY174: $i,SY175: $i] :
( ~ ( in @ SY174 @ A )
| ~ ( in @ SY175 @ A )
| ( ( in @ ( sK13_SY176 @ SY175 @ SY174 @ A ) @ ( sK12_B @ A ) )
& ( ~ ( in @ SY174 @ ( sK13_SY176 @ SY175 @ SY174 @ A ) )
| ~ ( in @ SY175 @ ( sK13_SY176 @ SY175 @ SY174 @ A ) ) )
& ( ( in @ SY174 @ ( sK13_SY176 @ SY175 @ SY174 @ A ) )
| ( in @ SY175 @ ( sK13_SY176 @ SY175 @ SY174 @ A ) ) ) )
| ( SY174 = SY175 ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(46,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK11_B @ A ) @ A )
& ! [SY159: $i] :
( ~ ( in @ SY159 @ ( sK11_B @ A ) )
| ~ ( in @ SY159 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(47,plain,
( ( ! [SY19: $i > $i > $o,SY20: $i] :
( ( ( in @ ( sK9_SY21 @ SY20 @ SY19 ) @ SY20 )
& ! [SY157: $i] :
( ( ( SY19 @ ( sK9_SY21 @ SY20 @ SY19 ) @ ( sK10_SY158 @ SY157 @ SY20 @ SY19 ) )
& ( SY157
!= ( sK10_SY158 @ SY157 @ SY20 @ SY19 ) ) )
| ~ ( SY19 @ ( sK9_SY21 @ SY20 @ SY19 ) @ SY157 ) ) )
| ( ! [SY153: $i] :
( ! [Xy: $i] :
( ~ ( SY19 @ Xy @ SY153 )
| ~ ( in @ Xy @ SY20 ) )
| ( in @ SY153 @ ( sK7_B @ SY20 @ SY19 ) ) )
& ! [SY155: $i] :
( ~ ( in @ SY155 @ ( sK7_B @ SY20 @ SY19 ) )
| ( ( SY19 @ ( sK8_Xy @ SY155 @ SY20 @ SY19 ) @ SY155 )
& ( in @ ( sK8_Xy @ SY155 @ SY20 @ SY19 ) @ SY20 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK6_Xx @ A ) @ omega )
& ( in @ ( sK6_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK6_Xx @ A ) @ ( sK6_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(49,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(50,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(51,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK5_B @ Xx @ A ) )
& ( in @ ( sK5_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK4_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK4_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(53,plain,
( ( ! [Xx: $i] :
( ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) )
& ! [A: $i,Xy: $i] :
( ( Xy != Xx )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
& ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(54,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK3_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK3_Xx @ B @ A ) @ A )
| ( in @ ( sK3_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(56,plain,
( ( ( in @ sK2_Xx @ emptyset )
& ~ sK1_Xphi )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(57,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK5_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK5_B @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(58,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ ( sK11_B @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK11_B @ SX0 ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(59,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK17_SY54 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(60,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ( ~ ( in @ ( sK9_SY21 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK9_SY21 @ SX1 @ SX0 ) @ ( sK10_SY158 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK10_SY158 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ ( sK9_SY21 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( SX0 @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX2 @ ( sK7_B @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK7_B @ SX1 @ SX0 ) )
| ~ ( ~ ( SX0 @ ( sK8_Xy @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK8_Xy @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(61,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(62,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK16_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK16_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK12_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( sK14_SY163 @ SX1 @ SX0 ) ) )
| ( in @ ( sK15_SY177 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SX1 @ SX0 ) @ ( sK12_B @ SX0 ) )
| ~ ( in @ ( sK15_SY177 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK14_SY163 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK12_B @ SX0 ) )
| ~ ( in @ SX2 @ ( sK12_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK12_B @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SX2 @ SX1 @ SX0 ) @ ( sK12_B @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ SX1 @ ( sK13_SY176 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK13_SY176 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( in @ SX1 @ ( sK13_SY176 @ SX2 @ SX1 @ SX0 ) )
| ( in @ SX2 @ ( sK13_SY176 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(63,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SX0 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SX0 ) @ ( sK6_Xx @ SX0 ) ) @ SX0 ) )
| ~ ( in @ emptyset @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(64,plain,
( ( ~ ( ~ ( in @ sK2_Xx @ emptyset )
| ~ ~ sK1_Xphi ) )
= $true ),
inference(unfold_def,[status(thm)],[56,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(66,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(67,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK19_SY71 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK19_SY71 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK18_Xx @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK18_Xx @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(68,plain,
! [SV1: $o] :
( ( ! [SY185: $i] :
~ ( in @ SY185
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY186: $i] : SV1 ) )
| SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[39]) ).
thf(69,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[39]) ).
thf(70,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[39]) ).
thf(71,plain,
! [SV2: $i] :
( ( ! [SY187: $i > $o,SY188: $i] :
( ~ ( in @ SY188
@ ( dsetconstr @ SV2
@ ^ [Xy: $i] : ( SY187 @ Xy ) ) )
| ( SY187 @ SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(72,plain,
! [SV3: $i] :
( ( ! [SY190: $i > $o,SY191: $i] :
( ~ ( in @ SY191
@ ( dsetconstr @ SV3
@ ^ [Xy: $i] : ( SY190 @ Xy ) ) )
| ( in @ SY191 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(73,plain,
! [SV4: $i] :
( ( ! [SY193: $i > $o,SY194: $i] :
( ~ ( in @ SY194 @ SV4 )
| ~ ( SY193 @ SY194 )
| ( in @ SY194
@ ( dsetconstr @ SV4
@ ^ [Xy: $i] : ( SY193 @ Xy ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(74,plain,
! [SV5: $i] :
( ( ~ ( in @ SV5 @ omega )
| ( in @ ( setadjoin @ SV5 @ SV5 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(75,plain,
! [SV6: $i] :
( ( ~ ( in @ SV6 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(76,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK5_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK5_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(77,plain,
! [SV7: $i] :
( ( ! [SY196: $i] :
~ ( in @ SY196 @ SV7 )
| ~ ( ~ ( in @ ( sK11_B @ SV7 ) @ SV7 )
| ~ ! [SY197: $i] :
( ~ ( in @ SY197 @ ( sK11_B @ SV7 ) )
| ~ ( in @ SY197 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(78,plain,
! [SV8: $i > $o] :
( ( ! [SY198: $i] :
( ~ ( ~ ( SV8 @ ( sK17_SY54 @ SY198 @ SV8 ) )
| ~ ( ( SY198
!= ( sK17_SY54 @ SY198 @ SV8 ) ) ) )
| ~ ( SV8 @ SY198 ) )
| ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(79,plain,
! [SV9: $i > $i > $o] :
( ( ! [SY200: $i] :
( ~ ( ~ ( in @ ( sK9_SY21 @ SY200 @ SV9 ) @ SY200 )
| ~ ! [SY201: $i] :
( ~ ( ~ ( SV9 @ ( sK9_SY21 @ SY200 @ SV9 ) @ ( sK10_SY158 @ SY201 @ SY200 @ SV9 ) )
| ~ ( ( SY201
!= ( sK10_SY158 @ SY201 @ SY200 @ SV9 ) ) ) )
| ~ ( SV9 @ ( sK9_SY21 @ SY200 @ SV9 ) @ SY201 ) ) )
| ~ ( ~ ! [SY202: $i] :
( ! [SY203: $i] :
( ~ ( SV9 @ SY203 @ SY202 )
| ~ ( in @ SY203 @ SY200 ) )
| ( in @ SY202 @ ( sK7_B @ SY200 @ SV9 ) ) )
| ~ ! [SY204: $i] :
( ~ ( in @ SY204 @ ( sK7_B @ SY200 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY204 @ SY200 @ SV9 ) @ SY204 )
| ~ ( in @ ( sK8_Xy @ SY204 @ SY200 @ SV9 ) @ SY200 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(80,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY205: $i,SY206: $i] :
( ~ ( in @ SY206 @ ( setadjoin @ SV10 @ SY205 ) )
| ( SY206 = SV10 )
| ( in @ SY206 @ SY205 ) )
| ~ ~ ( ~ ! [SY207: $i,SY208: $i] :
( ( SY208 != SV10 )
| ( in @ SY208 @ ( setadjoin @ SV10 @ SY207 ) ) )
| ~ ! [SY209: $i,SY210: $i] :
( ~ ( in @ SY210 @ SY209 )
| ( in @ SY210 @ ( setadjoin @ SV10 @ SY209 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(81,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY211: $i] :
( ~ ( ~ ( in @ ( sK16_Xx @ SY211 @ SV11 ) @ SY211 )
| ~ ~ ( in @ ( sK16_Xx @ SY211 @ SV11 ) @ SV11 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY211 )
| ~ ( ~ ! [SY213: $i] :
( ~ ( in @ SY213 @ ( sK12_B @ SV11 ) )
| ! [SY214: $i] :
( ~ ( in @ SY214 @ SY213 )
| ( in @ SY214 @ ( sK14_SY163 @ SY211 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SY211 @ SV11 ) @ SY213 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SY211 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SY211 @ SV11 ) @ SY211 ) )
| ~ ! [SY215: $i] :
( ~ ( in @ SY215 @ ( sK14_SY163 @ SY211 @ SV11 ) )
| ~ ( in @ SY215 @ SY211 ) ) ) ) )
| ~ ~ ( ~ ! [SY216: $i,SY217: $i] :
( ~ ( in @ SY216 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SY217 @ ( sK12_B @ SV11 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY216 )
| ( in @ SX3 @ SY217 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY217 )
| ( in @ SX3 @ SY216 ) ) )
| ~ ~ ( ~ ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) )
| ~ ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(82,plain,
! [SV12: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV12 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 ) )
| ~ ( in @ emptyset @ SV12 )
| ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(83,plain,
( ( ~ ( in @ sK2_Xx @ emptyset )
| ~ ~ sK1_Xphi )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(84,plain,
! [SV13: $i] :
( ( ! [SY225: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_Xx @ SY225 @ SV13 ) @ SV13 )
| ~ ( in @ ( sK3_Xx @ SY225 @ SV13 ) @ SY225 ) )
| ~ ( ( in @ ( sK3_Xx @ SY225 @ SV13 ) @ SV13 )
| ( in @ ( sK3_Xx @ SY225 @ SV13 ) @ SY225 ) ) )
| ( SV13 = SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(85,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(86,plain,
! [SV14: $i > $o] :
( ( ! [SY226: $i] :
( ~ ( ~ ( SV14 @ ( sK19_SY71 @ SY226 @ SV14 ) )
| ~ ( ( SY226
!= ( sK19_SY71 @ SY226 @ SV14 ) ) ) )
| ~ ( SV14 @ SY226 ) )
| ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(87,plain,
! [SV1: $o] :
( ( ( ! [SY185: $i] :
~ ( in @ SY185
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY186: $i] : SV1 ) ) )
= $true )
| ( SV1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(88,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(89,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(90,plain,
! [SV15: $i > $o,SV2: $i] :
( ( ! [SY228: $i] :
( ~ ( in @ SY228
@ ( dsetconstr @ SV2
@ ^ [SY229: $i] : ( SV15 @ SY229 ) ) )
| ( SV15 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(91,plain,
! [SV16: $i > $o,SV3: $i] :
( ( ! [SY230: $i] :
( ~ ( in @ SY230
@ ( dsetconstr @ SV3
@ ^ [SY231: $i] : ( SV16 @ SY231 ) ) )
| ( in @ SY230 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(92,plain,
! [SV17: $i > $o,SV4: $i] :
( ( ! [SY232: $i] :
( ~ ( in @ SY232 @ SV4 )
| ~ ( SV17 @ SY232 )
| ( in @ SY232
@ ( dsetconstr @ SV4
@ ^ [SY233: $i] : ( SV17 @ SY233 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(93,plain,
! [SV5: $i] :
( ( ( ~ ( in @ SV5 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV5 @ SV5 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(94,plain,
! [SV6: $i] :
( ( in @ SV6 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(95,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(96,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK5_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK5_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(97,plain,
! [SV7: $i] :
( ( ( ! [SY196: $i] :
~ ( in @ SY196 @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_B @ SV7 ) @ SV7 )
| ~ ! [SY197: $i] :
( ~ ( in @ SY197 @ ( sK11_B @ SV7 ) )
| ~ ( in @ SY197 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(98,plain,
! [SV8: $i > $o] :
( ( ( ! [SY198: $i] :
( ~ ( ~ ( SV8 @ ( sK17_SY54 @ SY198 @ SV8 ) )
| ~ ( ( SY198
!= ( sK17_SY54 @ SY198 @ SV8 ) ) ) )
| ~ ( SV8 @ SY198 ) ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(99,plain,
! [SV9: $i > $i > $o,SV18: $i] :
( ( ~ ( ~ ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
| ~ ! [SY234: $i] :
( ~ ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) )
| ~ ( ( SY234
!= ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) ) ) )
| ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(100,plain,
! [SV10: $i] :
( ( ~ ! [SY205: $i,SY206: $i] :
( ~ ( in @ SY206 @ ( setadjoin @ SV10 @ SY205 ) )
| ( SY206 = SV10 )
| ( in @ SY206 @ SY205 ) )
| ~ ~ ( ~ ! [SY207: $i,SY208: $i] :
( ( SY208 != SV10 )
| ( in @ SY208 @ ( setadjoin @ SV10 @ SY207 ) ) )
| ~ ! [SY209: $i,SY210: $i] :
( ~ ( in @ SY210 @ SY209 )
| ( in @ SY210 @ ( setadjoin @ SV10 @ SY209 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(101,plain,
! [SV11: $i] :
( ( ~ ! [SY211: $i] :
( ~ ( ~ ( in @ ( sK16_Xx @ SY211 @ SV11 ) @ SY211 )
| ~ ~ ( in @ ( sK16_Xx @ SY211 @ SV11 ) @ SV11 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY211 )
| ~ ( ~ ! [SY213: $i] :
( ~ ( in @ SY213 @ ( sK12_B @ SV11 ) )
| ! [SY214: $i] :
( ~ ( in @ SY214 @ SY213 )
| ( in @ SY214 @ ( sK14_SY163 @ SY211 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SY211 @ SV11 ) @ SY213 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SY211 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SY211 @ SV11 ) @ SY211 ) )
| ~ ! [SY215: $i] :
( ~ ( in @ SY215 @ ( sK14_SY163 @ SY211 @ SV11 ) )
| ~ ( in @ SY215 @ SY211 ) ) ) ) )
| ~ ~ ( ~ ! [SY216: $i,SY217: $i] :
( ~ ( in @ SY216 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SY217 @ ( sK12_B @ SV11 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY216 )
| ( in @ SX3 @ SY217 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY217 )
| ( in @ SX3 @ SY216 ) ) )
| ~ ~ ( ~ ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) )
| ~ ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(102,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV12 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 ) )
| ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(103,plain,
( ( ~ ( in @ sK2_Xx @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(104,plain,
( ( ~ ~ sK1_Xphi )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(105,plain,
! [SV13: $i,SV19: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) )
| ~ ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) ) )
| ( SV13 = SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(106,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(107,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(108,plain,
! [SV14: $i > $o] :
( ( ( ! [SY226: $i] :
( ~ ( ~ ( SV14 @ ( sK19_SY71 @ SY226 @ SV14 ) )
| ~ ( ( SY226
!= ( sK19_SY71 @ SY226 @ SV14 ) ) ) )
| ~ ( SV14 @ SY226 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(109,plain,
! [SV1: $o,SV20: $i] :
( ( ( ~ ( in @ SV20
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY186: $i] : SV1 ) ) )
= $true )
| ( SV1 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(110,plain,
! [SV21: $i] :
( ( ( ~ ( in @ SV21
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(111,plain,
! [SV22: $i] :
( ( ( ~ ( in @ SV22
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(112,plain,
! [SV15: $i > $o,SV2: $i,SV23: $i] :
( ( ~ ( in @ SV23
@ ( dsetconstr @ SV2
@ ^ [SY229: $i] : ( SV15 @ SY229 ) ) )
| ( SV15 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(113,plain,
! [SV16: $i > $o,SV3: $i,SV24: $i] :
( ( ~ ( in @ SV24
@ ( dsetconstr @ SV3
@ ^ [SY231: $i] : ( SV16 @ SY231 ) ) )
| ( in @ SV24 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(114,plain,
! [SV17: $i > $o,SV4: $i,SV25: $i] :
( ( ~ ( in @ SV25 @ SV4 )
| ~ ( SV17 @ SV25 )
| ( in @ SV25
@ ( dsetconstr @ SV4
@ ^ [SY233: $i] : ( SV17 @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(115,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV5 @ SV5 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK5_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK5_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(118,plain,
! [SV7: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_B @ SV7 ) @ SV7 )
| ~ ! [SY197: $i] :
( ~ ( in @ SY197 @ ( sK11_B @ SV7 ) )
| ~ ( in @ SY197 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(119,plain,
! [SV27: $i,SV8: $i > $o] :
( ( ( ~ ( ~ ( SV8 @ ( sK17_SY54 @ SV27 @ SV8 ) )
| ~ ( ( SV27
!= ( sK17_SY54 @ SV27 @ SV8 ) ) ) )
| ~ ( SV8 @ SV27 ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(120,plain,
! [SV9: $i > $i > $o,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
| ~ ! [SY234: $i] :
( ~ ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) )
| ~ ( ( SY234
!= ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) ) ) )
| ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SY234 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(121,plain,
! [SV10: $i] :
( ( ~ ! [SY205: $i,SY206: $i] :
( ~ ( in @ SY206 @ ( setadjoin @ SV10 @ SY205 ) )
| ( SY206 = SV10 )
| ( in @ SY206 @ SY205 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(122,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ! [SY207: $i,SY208: $i] :
( ( SY208 != SV10 )
| ( in @ SY208 @ ( setadjoin @ SV10 @ SY207 ) ) )
| ~ ! [SY209: $i,SY210: $i] :
( ~ ( in @ SY210 @ SY209 )
| ( in @ SY210 @ ( setadjoin @ SV10 @ SY209 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(123,plain,
! [SV11: $i] :
( ( ~ ! [SY211: $i] :
( ~ ( ~ ( in @ ( sK16_Xx @ SY211 @ SV11 ) @ SY211 )
| ~ ~ ( in @ ( sK16_Xx @ SY211 @ SV11 ) @ SV11 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY211 )
| ~ ( ~ ! [SY213: $i] :
( ~ ( in @ SY213 @ ( sK12_B @ SV11 ) )
| ! [SY214: $i] :
( ~ ( in @ SY214 @ SY213 )
| ( in @ SY214 @ ( sK14_SY163 @ SY211 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SY211 @ SV11 ) @ SY213 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SY211 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SY211 @ SV11 ) @ SY211 ) )
| ~ ! [SY215: $i] :
( ~ ( in @ SY215 @ ( sK14_SY163 @ SY211 @ SV11 ) )
| ~ ( in @ SY215 @ SY211 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(124,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ! [SY216: $i,SY217: $i] :
( ~ ( in @ SY216 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SY217 @ ( sK12_B @ SV11 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY216 )
| ( in @ SX3 @ SY217 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY217 )
| ( in @ SX3 @ SY216 ) ) )
| ~ ~ ( ~ ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) )
| ~ ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(125,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV12 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(126,plain,
( ( in @ sK2_Xx @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(127,plain,
( ( ~ sK1_Xphi ) = $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(128,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) )
| ~ ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) ) ) )
= $true )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(131,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ( ~ ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
| ~ ( ( SV28
!= ( sK19_SY71 @ SV28 @ SV14 ) ) ) )
| ~ ( SV14 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(132,plain,
! [SV1: $o,SV20: $i] :
( ( ( in @ SV20
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY186: $i] : SV1 ) )
= $false )
| ( SV1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(133,plain,
! [SV21: $i] :
( ( ( in @ SV21
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(134,plain,
! [SV22: $i] :
( ( ( in @ SV22
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(135,plain,
! [SV15: $i > $o,SV2: $i,SV23: $i] :
( ( ( ~ ( in @ SV23
@ ( dsetconstr @ SV2
@ ^ [SY229: $i] : ( SV15 @ SY229 ) ) ) )
= $true )
| ( ( SV15 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(136,plain,
! [SV16: $i > $o,SV3: $i,SV24: $i] :
( ( ( ~ ( in @ SV24
@ ( dsetconstr @ SV3
@ ^ [SY231: $i] : ( SV16 @ SY231 ) ) ) )
= $true )
| ( ( in @ SV24 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(137,plain,
! [SV17: $i > $o,SV4: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV4 ) )
= $true )
| ( ( ~ ( SV17 @ SV25 )
| ( in @ SV25
@ ( dsetconstr @ SV4
@ ^ [SY233: $i] : ( SV17 @ SY233 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(138,plain,
! [SV29: $i] :
( ( ! [SY244: $i] :
( ! [SY245: $i] :
( ~ ( in @ SY244 @ SY245 )
| ~ ( in @ SY245 @ SV29 ) )
| ( in @ SY244 @ ( setunion @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(139,plain,
! [SV30: $i] :
( ( ! [SY246: $i] :
( ~ ( in @ SY246 @ ( setunion @ SV30 ) )
| ~ ( ~ ( in @ SY246 @ ( sK5_B @ SY246 @ SV30 ) )
| ~ ( in @ ( sK5_B @ SY246 @ SV30 ) @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(140,plain,
! [SV7: $i,SV26: $i] :
( ( ( in @ SV26 @ SV7 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_B @ SV7 ) @ SV7 )
| ~ ! [SY197: $i] :
( ~ ( in @ SY197 @ ( sK11_B @ SV7 ) )
| ~ ( in @ SY197 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(141,plain,
! [SV27: $i,SV8: $i > $o] :
( ( ( ~ ( ~ ( SV8 @ ( sK17_SY54 @ SV27 @ SV8 ) )
| ~ ( ( SV27
!= ( sK17_SY54 @ SV27 @ SV8 ) ) ) ) )
= $true )
| ( ( ~ ( SV8 @ SV27 ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(142,plain,
! [SV9: $i > $i > $o,SV18: $i] :
( ( ( ~ ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
| ~ ! [SY234: $i] :
( ~ ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) )
| ~ ( ( SY234
!= ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) ) ) )
| ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SY234 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(143,plain,
! [SV10: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ~ ( in @ SY206 @ ( setadjoin @ SV10 @ SY205 ) )
| ( SY206 = SV10 )
| ( in @ SY206 @ SY205 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(144,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY207: $i,SY208: $i] :
( ( SY208 != SV10 )
| ( in @ SY208 @ ( setadjoin @ SV10 @ SY207 ) ) )
| ~ ! [SY209: $i,SY210: $i] :
( ~ ( in @ SY210 @ SY209 )
| ( in @ SY210 @ ( setadjoin @ SV10 @ SY209 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(145,plain,
! [SV11: $i] :
( ( ! [SY211: $i] :
( ~ ( ~ ( in @ ( sK16_Xx @ SY211 @ SV11 ) @ SY211 )
| ~ ~ ( in @ ( sK16_Xx @ SY211 @ SV11 ) @ SV11 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY211 )
| ~ ( ~ ! [SY213: $i] :
( ~ ( in @ SY213 @ ( sK12_B @ SV11 ) )
| ! [SY214: $i] :
( ~ ( in @ SY214 @ SY213 )
| ( in @ SY214 @ ( sK14_SY163 @ SY211 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SY211 @ SV11 ) @ SY213 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SY211 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SY211 @ SV11 ) @ SY211 ) )
| ~ ! [SY215: $i] :
( ~ ( in @ SY215 @ ( sK14_SY163 @ SY211 @ SV11 ) )
| ~ ( in @ SY215 @ SY211 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(146,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY216: $i,SY217: $i] :
( ~ ( in @ SY216 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SY217 @ ( sK12_B @ SV11 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY216 )
| ( in @ SX3 @ SY217 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY217 )
| ( in @ SX3 @ SY216 ) ) )
| ~ ~ ( ~ ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) )
| ~ ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(147,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV12 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(148,plain,
sK1_Xphi = $false,
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(149,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) )
| ~ ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) ) )
= $false )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV31: $i] :
( ( ! [SY247: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SY247 @ SV31 ) @ SY247 )
| ~ ~ ( in @ ( sK4_Xx @ SY247 @ SV31 ) @ SV31 ) )
| ( in @ SY247 @ ( powerset @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(151,plain,
! [SV32: $i] :
( ( ! [SY248: $i] :
( ~ ( in @ SY248 @ ( powerset @ SV32 ) )
| ! [SY249: $i] :
( ~ ( in @ SY249 @ SY248 )
| ( in @ SY249 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(152,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ( ~ ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
| ~ ( ( SV28
!= ( sK19_SY71 @ SV28 @ SV14 ) ) ) ) )
= $true )
| ( ( ~ ( SV14 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(153,plain,
! [SV15: $i > $o,SV2: $i,SV23: $i] :
( ( ( in @ SV23
@ ( dsetconstr @ SV2
@ ^ [SY229: $i] : ( SV15 @ SY229 ) ) )
= $false )
| ( ( SV15 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(154,plain,
! [SV16: $i > $o,SV3: $i,SV24: $i] :
( ( ( in @ SV24
@ ( dsetconstr @ SV3
@ ^ [SY231: $i] : ( SV16 @ SY231 ) ) )
= $false )
| ( ( in @ SV24 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(155,plain,
! [SV17: $i > $o,SV4: $i,SV25: $i] :
( ( ( in @ SV25 @ SV4 )
= $false )
| ( ( ~ ( SV17 @ SV25 )
| ( in @ SV25
@ ( dsetconstr @ SV4
@ ^ [SY233: $i] : ( SV17 @ SY233 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(156,plain,
! [SV29: $i,SV33: $i] :
( ( ! [SY250: $i] :
( ~ ( in @ SV33 @ SY250 )
| ~ ( in @ SY250 @ SV29 ) )
| ( in @ SV33 @ ( setunion @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(157,plain,
! [SV30: $i,SV34: $i] :
( ( ~ ( in @ SV34 @ ( setunion @ SV30 ) )
| ~ ( ~ ( in @ SV34 @ ( sK5_B @ SV34 @ SV30 ) )
| ~ ( in @ ( sK5_B @ SV34 @ SV30 ) @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(158,plain,
! [SV26: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK11_B @ SV7 ) @ SV7 )
| ~ ! [SY197: $i] :
( ~ ( in @ SY197 @ ( sK11_B @ SV7 ) )
| ~ ( in @ SY197 @ SV7 ) ) )
= $false )
| ( ( in @ SV26 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(159,plain,
! [SV27: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ ( sK17_SY54 @ SV27 @ SV8 ) )
| ~ ( ( SV27
!= ( sK17_SY54 @ SV27 @ SV8 ) ) ) )
= $false )
| ( ( ~ ( SV8 @ SV27 ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(160,plain,
! [SV9: $i > $i > $o,SV18: $i] :
( ( ( ~ ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(161,plain,
! [SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ! [SY234: $i] :
( ~ ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) )
| ~ ( ( SY234
!= ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) ) ) )
| ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SY234 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(162,plain,
! [SV35: $i,SV10: $i] :
( ( ! [SY251: $i] :
( ~ ( in @ SY251 @ ( setadjoin @ SV10 @ SV35 ) )
| ( SY251 = SV10 )
| ( in @ SY251 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(163,plain,
! [SV10: $i] :
( ( ~ ! [SY207: $i,SY208: $i] :
( ( SY208 != SV10 )
| ( in @ SY208 @ ( setadjoin @ SV10 @ SY207 ) ) )
| ~ ! [SY209: $i,SY210: $i] :
( ~ ( in @ SY210 @ SY209 )
| ( in @ SY210 @ ( setadjoin @ SV10 @ SY209 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(164,plain,
! [SV11: $i,SV36: $i] :
( ( ~ ( ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
| ~ ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 ) )
| ! [SY252: $i] :
~ ( in @ SY252 @ SV36 )
| ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(165,plain,
! [SV11: $i] :
( ( ~ ! [SY216: $i,SY217: $i] :
( ~ ( in @ SY216 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SY217 @ ( sK12_B @ SV11 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY216 )
| ( in @ SX3 @ SY217 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY217 )
| ( in @ SX3 @ SY216 ) ) )
| ~ ~ ( ~ ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) )
| ~ ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(166,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV12 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV12 ) @ SV12 ) ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(167,plain,
! [SV12: $i] :
( ( ( ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(168,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) ) )
= $false )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(169,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) ) )
= $false )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(170,plain,
! [SV31: $i,SV37: $i] :
( ( ~ ( ~ ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV37 )
| ~ ~ ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV31 ) )
| ( in @ SV37 @ ( powerset @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(171,plain,
! [SV32: $i,SV38: $i] :
( ( ~ ( in @ SV38 @ ( powerset @ SV32 ) )
| ! [SY256: $i] :
( ~ ( in @ SY256 @ SV38 )
| ( in @ SY256 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(172,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
| ~ ( ( SV28
!= ( sK19_SY71 @ SV28 @ SV14 ) ) ) )
= $false )
| ( ( ~ ( SV14 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(173,plain,
! [SV4: $i,SV25: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ SV25 ) )
= $true )
| ( ( in @ SV25
@ ( dsetconstr @ SV4
@ ^ [SY233: $i] : ( SV17 @ SY233 ) ) )
= $true )
| ( ( in @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(174,plain,
! [SV29: $i,SV33: $i] :
( ( ( ! [SY250: $i] :
( ~ ( in @ SV33 @ SY250 )
| ~ ( in @ SY250 @ SV29 ) ) )
= $true )
| ( ( in @ SV33 @ ( setunion @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(175,plain,
! [SV30: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ ( setunion @ SV30 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV34 @ ( sK5_B @ SV34 @ SV30 ) )
| ~ ( in @ ( sK5_B @ SV34 @ SV30 ) @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(176,plain,
! [SV26: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK11_B @ SV7 ) @ SV7 ) )
= $false )
| ( ( in @ SV26 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(177,plain,
! [SV26: $i,SV7: $i] :
( ( ( ~ ! [SY197: $i] :
( ~ ( in @ SY197 @ ( sK11_B @ SV7 ) )
| ~ ( in @ SY197 @ SV7 ) ) )
= $false )
| ( ( in @ SV26 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(178,plain,
! [SV27: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ ( sK17_SY54 @ SV27 @ SV8 ) ) )
= $false )
| ( ( ~ ( SV8 @ SV27 ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(179,plain,
! [SV8: $i > $o,SV27: $i] :
( ( ( ~ ( ( SV27
!= ( sK17_SY54 @ SV27 @ SV8 ) ) ) )
= $false )
| ( ( ~ ( SV8 @ SV27 ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(180,plain,
! [SV9: $i > $i > $o,SV18: $i] :
( ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(181,plain,
! [SV18: $i,SV9: $i > $i > $o] :
( ( ( ! [SY234: $i] :
( ~ ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) )
| ~ ( ( SY234
!= ( sK10_SY158 @ SY234 @ SV18 @ SV9 ) ) ) )
| ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SY234 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(182,plain,
! [SV35: $i,SV10: $i,SV39: $i] :
( ( ~ ( in @ SV39 @ ( setadjoin @ SV10 @ SV35 ) )
| ( SV39 = SV10 )
| ( in @ SV39 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(183,plain,
! [SV10: $i] :
( ( ~ ! [SY207: $i,SY208: $i] :
( ( SY208 != SV10 )
| ( in @ SY208 @ ( setadjoin @ SV10 @ SY207 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(184,plain,
! [SV10: $i] :
( ( ~ ! [SY209: $i,SY210: $i] :
( ~ ( in @ SY210 @ SY209 )
| ( in @ SY210 @ ( setadjoin @ SV10 @ SY209 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(185,plain,
! [SV11: $i,SV36: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
| ~ ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 ) )
| ! [SY252: $i] :
~ ( in @ SY252 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(186,plain,
! [SV11: $i] :
( ( ~ ! [SY216: $i,SY217: $i] :
( ~ ( in @ SY216 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SY217 @ ( sK12_B @ SV11 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY216 )
| ( in @ SX3 @ SY217 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY217 )
| ( in @ SX3 @ SY216 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(187,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) )
| ~ ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(188,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_Xx @ SV12 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(189,plain,
! [SV12: $i] :
( ( ( ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(190,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) )
= $true )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(191,plain,
! [SV13: $i,SV19: $i] :
( ( ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
| ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) )
= $true )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(192,plain,
! [SV31: $i,SV37: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV37 )
| ~ ~ ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV31 ) ) )
= $true )
| ( ( in @ SV37 @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(193,plain,
! [SV32: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( ! [SY256: $i] :
( ~ ( in @ SY256 @ SV38 )
| ( in @ SY256 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(194,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) ) )
= $false )
| ( ( ~ ( SV14 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(195,plain,
! [SV14: $i > $o,SV28: $i] :
( ( ( ~ ( ( SV28
!= ( sK19_SY71 @ SV28 @ SV14 ) ) ) )
= $false )
| ( ( ~ ( SV14 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(196,plain,
! [SV4: $i,SV25: $i,SV17: $i > $o] :
( ( ( SV17 @ SV25 )
= $false )
| ( ( in @ SV25
@ ( dsetconstr @ SV4
@ ^ [SY233: $i] : ( SV17 @ SY233 ) ) )
= $true )
| ( ( in @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(197,plain,
! [SV29: $i,SV40: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV40 )
| ~ ( in @ SV40 @ SV29 ) )
= $true )
| ( ( in @ SV33 @ ( setunion @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV30: $i,SV34: $i] :
( ( ( in @ SV34 @ ( setunion @ SV30 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV34 @ ( sK5_B @ SV34 @ SV30 ) )
| ~ ( in @ ( sK5_B @ SV34 @ SV30 ) @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV26: $i,SV7: $i] :
( ( ( in @ ( sK11_B @ SV7 ) @ SV7 )
= $true )
| ( ( in @ SV26 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(200,plain,
! [SV26: $i,SV7: $i] :
( ( ( ! [SY197: $i] :
( ~ ( in @ SY197 @ ( sK11_B @ SV7 ) )
| ~ ( in @ SY197 @ SV7 ) ) )
= $true )
| ( ( in @ SV26 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(201,plain,
! [SV27: $i,SV8: $i > $o] :
( ( ( SV8 @ ( sK17_SY54 @ SV27 @ SV8 ) )
= $true )
| ( ( ~ ( SV8 @ SV27 ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(202,plain,
! [SV8: $i > $o,SV27: $i] :
( ( ( SV27
!= ( sK17_SY54 @ SV27 @ SV8 ) )
= $true )
| ( ( ~ ( SV8 @ SV27 ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(203,plain,
! [SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(204,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
| ~ ( ( SV41
!= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) ) ) )
| ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(205,plain,
! [SV35: $i,SV10: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( setadjoin @ SV10 @ SV35 ) ) )
= $true )
| ( ( ( SV39 = SV10 )
| ( in @ SV39 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(206,plain,
! [SV10: $i] :
( ( ! [SY207: $i,SY208: $i] :
( ( SY208 != SV10 )
| ( in @ SY208 @ ( setadjoin @ SV10 @ SY207 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(207,plain,
! [SV10: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ~ ( in @ SY210 @ SY209 )
| ( in @ SY210 @ ( setadjoin @ SV10 @ SY209 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(208,plain,
! [SV11: $i,SV36: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
| ~ ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( ! [SY252: $i] :
~ ( in @ SY252 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(209,plain,
! [SV11: $i] :
( ( ! [SY216: $i,SY217: $i] :
( ~ ( in @ SY216 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SY217 @ ( sK12_B @ SV11 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY216 )
| ( in @ SX3 @ SY217 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY217 )
| ( in @ SX3 @ SY216 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(210,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) )
| ~ ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(211,plain,
! [SV12: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV12 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV12 ) @ SV12 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(212,plain,
! [SV12: $i] :
( ( ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 )
= $false )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(213,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 ) )
= $true )
| ( ( ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) )
= $true )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(214,plain,
! [SV13: $i,SV19: $i] :
( ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
= $true )
| ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 )
= $true )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(215,plain,
! [SV31: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV37 )
| ~ ~ ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV31 ) )
= $false )
| ( ( in @ SV37 @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(216,plain,
! [SV32: $i,SV38: $i] :
( ( ( in @ SV38 @ ( powerset @ SV32 ) )
= $false )
| ( ( ! [SY256: $i] :
( ~ ( in @ SY256 @ SV38 )
| ( in @ SY256 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(217,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( ~ ( SV14 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(218,plain,
! [SV14: $i > $o,SV28: $i] :
( ( ( SV28
!= ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( ~ ( SV14 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(219,plain,
! [SV29: $i,SV40: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV40 ) )
= $true )
| ( ( ~ ( in @ SV40 @ SV29 ) )
= $true )
| ( ( in @ SV33 @ ( setunion @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(220,plain,
! [SV30: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ ( sK5_B @ SV34 @ SV30 ) )
| ~ ( in @ ( sK5_B @ SV34 @ SV30 ) @ SV30 ) )
= $false )
| ( ( in @ SV34 @ ( setunion @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(221,plain,
! [SV26: $i,SV7: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ ( sK11_B @ SV7 ) )
| ~ ( in @ SV42 @ SV7 ) )
= $true )
| ( ( in @ SV26 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(222,plain,
! [SV27: $i,SV8: $i > $o] :
( ( ( SV8 @ SV27 )
= $false )
| ( ( SV8 @ ( sK17_SY54 @ SV27 @ SV8 ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(223,plain,
! [SV8: $i > $o,SV27: $i] :
( ( ( SV27
= ( sK17_SY54 @ SV27 @ SV8 ) )
= $false )
| ( ( ~ ( SV8 @ SV27 ) )
= $true )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(224,plain,
! [SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(225,plain,
! [SV9: $i > $i > $o,SV18: $i] :
( ( ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(226,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
| ~ ( ( SV41
!= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) ) ) ) )
= $true )
| ( ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(227,plain,
! [SV35: $i,SV10: $i,SV39: $i] :
( ( ( in @ SV39 @ ( setadjoin @ SV10 @ SV35 ) )
= $false )
| ( ( ( SV39 = SV10 )
| ( in @ SV39 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(228,plain,
! [SV43: $i,SV10: $i] :
( ( ! [SY257: $i] :
( ( SY257 != SV10 )
| ( in @ SY257 @ ( setadjoin @ SV10 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(229,plain,
! [SV10: $i,SV44: $i] :
( ( ! [SY258: $i] :
( ~ ( in @ SY258 @ SV44 )
| ( in @ SY258 @ ( setadjoin @ SV10 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(230,plain,
! [SV11: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
| ~ ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 ) )
= $false )
| ( ( ! [SY252: $i] :
~ ( in @ SY252 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(231,plain,
! [SV11: $i,SV45: $i] :
( ( ! [SY259: $i] :
( ~ ( in @ SV45 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SY259 @ ( sK12_B @ SV11 ) )
| ! [SY260: $i] :
( ~ ( in @ SY260 @ SV45 )
| ( in @ SY260 @ SY259 ) )
| ! [SY261: $i] :
( ~ ( in @ SY261 @ SY259 )
| ( in @ SY261 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(232,plain,
! [SV11: $i] :
( ( ~ ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) )
| ~ ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(233,plain,
! [SV12: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV12 ) @ omega ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(234,plain,
! [SV12: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV12 ) @ SV12 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(235,plain,
! [SV12: $i] :
( ( ( in @ emptyset @ SV12 )
= $false )
| ( ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 )
= $false )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(236,plain,
! [SV13: $i,SV19: $i] :
( ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
= $false )
| ( ( ~ ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 ) )
= $true )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(237,plain,
! [SV31: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV37 ) )
= $false )
| ( ( in @ SV37 @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(238,plain,
! [SV31: $i,SV37: $i] :
( ( ( ~ ~ ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV31 ) )
= $false )
| ( ( in @ SV37 @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(239,plain,
! [SV32: $i,SV38: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV38 )
| ( in @ SV46 @ SV32 ) )
= $true )
| ( ( in @ SV38 @ ( powerset @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(240,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( SV14 @ SV28 )
= $false )
| ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(241,plain,
! [SV14: $i > $o,SV28: $i] :
( ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( ~ ( SV14 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(242,plain,
! [SV29: $i,SV40: $i,SV33: $i] :
( ( ( in @ SV33 @ SV40 )
= $false )
| ( ( ~ ( in @ SV40 @ SV29 ) )
= $true )
| ( ( in @ SV33 @ ( setunion @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(243,plain,
! [SV30: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ ( sK5_B @ SV34 @ SV30 ) ) )
= $false )
| ( ( in @ SV34 @ ( setunion @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(244,plain,
! [SV30: $i,SV34: $i] :
( ( ( ~ ( in @ ( sK5_B @ SV34 @ SV30 ) @ SV30 ) )
= $false )
| ( ( in @ SV34 @ ( setunion @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(245,plain,
! [SV26: $i,SV7: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ ( sK11_B @ SV7 ) ) )
= $true )
| ( ( ~ ( in @ SV42 @ SV7 ) )
= $true )
| ( ( in @ SV26 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(246,plain,
! [SV27: $i,SV8: $i > $o] :
( ( ( SV8 @ SV27 )
= $false )
| ( ( SV27
= ( sK17_SY54 @ SV27 @ SV8 ) )
= $false )
| ( ( SV8
@ ( descr
@ ^ [SY199: $i] : ( SV8 @ SY199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(247,plain,
! [SV18: $i,SV9: $i > $i > $o] :
( ( ( ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(248,plain,
! [SV9: $i > $i > $o,SV18: $i] :
( ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(249,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
| ~ ( ( SV41
!= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) ) ) )
= $false )
| ( ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(250,plain,
! [SV35: $i,SV10: $i,SV39: $i] :
( ( ( SV39 = SV10 )
= $true )
| ( ( in @ SV39 @ SV35 )
= $true )
| ( ( in @ SV39 @ ( setadjoin @ SV10 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(251,plain,
! [SV43: $i,SV10: $i,SV47: $i] :
( ( ( SV47 != SV10 )
| ( in @ SV47 @ ( setadjoin @ SV10 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(252,plain,
! [SV10: $i,SV44: $i,SV48: $i] :
( ( ~ ( in @ SV48 @ SV44 )
| ( in @ SV48 @ ( setadjoin @ SV10 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(253,plain,
! [SV11: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 ) )
= $false )
| ( ( ! [SY252: $i] :
~ ( in @ SY252 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(254,plain,
! [SV11: $i,SV36: $i] :
( ( ( ~ ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 ) )
= $false )
| ( ( ! [SY252: $i] :
~ ( in @ SY252 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(255,plain,
! [SV49: $i,SV11: $i,SV45: $i] :
( ( ~ ( in @ SV45 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SV49 @ ( sK12_B @ SV11 ) )
| ! [SY262: $i] :
( ~ ( in @ SY262 @ SV45 )
| ( in @ SY262 @ SV49 ) )
| ! [SY263: $i] :
( ~ ( in @ SY263 @ SV49 )
| ( in @ SY263 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(256,plain,
! [SV11: $i] :
( ( ~ ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(257,plain,
! [SV11: $i] :
( ( ~ ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(258,plain,
! [SV12: $i] :
( ( ( in @ ( sK6_Xx @ SV12 ) @ omega )
= $true )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(259,plain,
! [SV12: $i] :
( ( ( in @ ( sK6_Xx @ SV12 ) @ SV12 )
= $true )
| ( ( ~ ( in @ emptyset @ SV12 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(260,plain,
! [SV12: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ omega )
| ( in @ SV50 @ SV12 ) )
= $true )
| ( ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 )
= $false )
| ( ( in @ emptyset @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(261,plain,
! [SV13: $i,SV19: $i] :
( ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV19 )
= $false )
| ( ( in @ ( sK3_Xx @ SV19 @ SV13 ) @ SV13 )
= $false )
| ( ( SV13 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(262,plain,
! [SV31: $i,SV37: $i] :
( ( ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV37 )
= $true )
| ( ( in @ SV37 @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(263,plain,
! [SV31: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV31 ) )
= $true )
| ( ( in @ SV37 @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(264,plain,
! [SV32: $i,SV38: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV38 ) )
= $true )
| ( ( in @ SV46 @ SV32 )
= $true )
| ( ( in @ SV38 @ ( powerset @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(265,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) )
= $false )
| ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(266,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( SV14 @ SV28 )
= $false )
| ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(267,plain,
! [SV33: $i,SV29: $i,SV40: $i] :
( ( ( in @ SV40 @ SV29 )
= $false )
| ( ( in @ SV33 @ SV40 )
= $false )
| ( ( in @ SV33 @ ( setunion @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(268,plain,
! [SV30: $i,SV34: $i] :
( ( ( in @ SV34 @ ( sK5_B @ SV34 @ SV30 ) )
= $true )
| ( ( in @ SV34 @ ( setunion @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(269,plain,
! [SV30: $i,SV34: $i] :
( ( ( in @ ( sK5_B @ SV34 @ SV30 ) @ SV30 )
= $true )
| ( ( in @ SV34 @ ( setunion @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(270,plain,
! [SV26: $i,SV7: $i,SV42: $i] :
( ( ( in @ SV42 @ ( sK11_B @ SV7 ) )
= $false )
| ( ( ~ ( in @ SV42 @ SV7 ) )
= $true )
| ( ( in @ SV26 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(271,plain,
! [SV18: $i,SV51: $i,SV9: $i > $i > $o] :
( ( ( ! [SY264: $i] :
( ~ ( SV9 @ SY264 @ SV51 )
| ~ ( in @ SY264 @ SV18 ) )
| ( in @ SV51 @ ( sK7_B @ SV18 @ SV9 ) ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(272,plain,
! [SV9: $i > $i > $o,SV18: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV52 )
| ~ ( in @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(273,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) ) )
= $false )
| ( ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(274,plain,
! [SV9: $i > $i > $o,SV18: $i,SV41: $i] :
( ( ( ~ ( ( SV41
!= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) ) ) )
= $false )
| ( ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(275,plain,
! [SV43: $i,SV10: $i,SV47: $i] :
( ( ( SV47 != SV10 )
= $true )
| ( ( in @ SV47 @ ( setadjoin @ SV10 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(276,plain,
! [SV10: $i,SV44: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV44 ) )
= $true )
| ( ( in @ SV48 @ ( setadjoin @ SV10 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(277,plain,
! [SV11: $i,SV36: $i] :
( ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( ! [SY252: $i] :
~ ( in @ SY252 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(278,plain,
! [SV11: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 ) )
= $true )
| ( ( ! [SY252: $i] :
~ ( in @ SY252 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(279,plain,
! [SV49: $i,SV11: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ ( sK12_B @ SV11 ) )
| ~ ( in @ SV49 @ ( sK12_B @ SV11 ) ) )
= $true )
| ( ( ! [SY262: $i] :
( ~ ( in @ SY262 @ SV45 )
| ( in @ SY262 @ SV49 ) )
| ! [SY263: $i] :
( ~ ( in @ SY263 @ SV49 )
| ( in @ SY263 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(280,plain,
! [SV11: $i] :
( ( ! [SY220: $i] :
( ~ ( in @ SY220 @ ( sK12_B @ SV11 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SY220 )
| ( in @ SY221 @ SV11 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(281,plain,
! [SV11: $i] :
( ( ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY222 @ SV11 )
| ~ ( in @ SY223 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ~ ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) )
| ~ ( ( in @ SY222 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) )
| ( in @ SY223 @ ( sK13_SY176 @ SY223 @ SY222 @ SV11 ) ) ) ) )
| ( SY222 = SY223 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(282,plain,
! [SV12: $i] :
( ( ( in @ emptyset @ SV12 )
= $false )
| ( ( in @ ( sK6_Xx @ SV12 ) @ omega )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(283,plain,
! [SV12: $i] :
( ( ( in @ emptyset @ SV12 )
= $false )
| ( ( in @ ( sK6_Xx @ SV12 ) @ SV12 )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( in @ SY224 @ omega )
| ( in @ SY224 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(284,plain,
! [SV12: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ omega ) )
= $true )
| ( ( in @ SV50 @ SV12 )
= $true )
| ( ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 )
= $false )
| ( ( in @ emptyset @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(285,plain,
! [SV31: $i,SV37: $i] :
( ( ( in @ ( sK4_Xx @ SV37 @ SV31 ) @ SV31 )
= $false )
| ( ( in @ SV37 @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(286,plain,
! [SV32: $i,SV38: $i,SV46: $i] :
( ( ( in @ SV46 @ SV38 )
= $false )
| ( ( in @ SV46 @ SV32 )
= $true )
| ( ( in @ SV38 @ ( powerset @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(287,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) ) )
= $false )
| ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(288,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) )
= $false )
| ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(289,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) )
| ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) )
= $false )
| ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(290,plain,
! [SV26: $i,SV7: $i,SV42: $i] :
( ( ( in @ SV42 @ SV7 )
= $false )
| ( ( in @ SV42 @ ( sK11_B @ SV7 ) )
= $false )
| ( ( in @ SV26 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(291,plain,
! [SV18: $i,SV51: $i,SV9: $i > $i > $o] :
( ( ( ! [SY264: $i] :
( ~ ( SV9 @ SY264 @ SV51 )
| ~ ( in @ SY264 @ SV18 ) ) )
= $true )
| ( ( in @ SV51 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(292,plain,
! [SV9: $i > $i > $o,SV18: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ ( sK7_B @ SV18 @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ( SV9 @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV52 )
| ~ ( in @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(293,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(294,plain,
! [SV9: $i > $i > $o,SV18: $i,SV41: $i] :
( ( ( SV41
!= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(295,plain,
! [SV43: $i,SV10: $i,SV47: $i] :
( ( ( SV47 = SV10 )
= $false )
| ( ( in @ SV47 @ ( setadjoin @ SV10 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(296,plain,
! [SV10: $i,SV44: $i,SV48: $i] :
( ( ( in @ SV48 @ SV44 )
= $false )
| ( ( in @ SV48 @ ( setadjoin @ SV10 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(297,plain,
! [SV11: $i,SV36: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV36 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(298,plain,
! [SV11: $i,SV36: $i] :
( ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( ! [SY252: $i] :
~ ( in @ SY252 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(299,plain,
! [SV49: $i,SV11: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ ( sK12_B @ SV11 ) ) )
= $true )
| ( ( ~ ( in @ SV49 @ ( sK12_B @ SV11 ) ) )
= $true )
| ( ( ! [SY262: $i] :
( ~ ( in @ SY262 @ SV45 )
| ( in @ SY262 @ SV49 ) )
| ! [SY263: $i] :
( ~ ( in @ SY263 @ SV49 )
| ( in @ SY263 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(300,plain,
! [SV11: $i,SV54: $i] :
( ( ~ ( in @ SV54 @ ( sK12_B @ SV11 ) )
| ! [SY265: $i] :
( ~ ( in @ SY265 @ SV54 )
| ( in @ SY265 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(301,plain,
! [SV11: $i,SV55: $i] :
( ( ! [SY266: $i] :
( ~ ( in @ SV55 @ SV11 )
| ~ ( in @ SY266 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SY266 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SY266 @ SV55 @ SV11 ) )
| ~ ( in @ SY266 @ ( sK13_SY176 @ SY266 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SY266 @ SV55 @ SV11 ) )
| ( in @ SY266 @ ( sK13_SY176 @ SY266 @ SV55 @ SV11 ) ) ) ) )
| ( SV55 = SY266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(302,plain,
! [SV12: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ omega )
| ( in @ SV56 @ SV12 ) )
= $true )
| ( ( in @ ( sK6_Xx @ SV12 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(303,plain,
! [SV12: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ omega )
| ( in @ SV57 @ SV12 ) )
= $true )
| ( ( in @ ( sK6_Xx @ SV12 ) @ SV12 )
= $true )
| ( ( in @ emptyset @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(304,plain,
! [SV12: $i,SV50: $i] :
( ( ( in @ SV50 @ omega )
= $false )
| ( ( in @ SV50 @ SV12 )
= $true )
| ( ( in @ ( setadjoin @ ( sK6_Xx @ SV12 ) @ ( sK6_Xx @ SV12 ) ) @ SV12 )
= $false )
| ( ( in @ emptyset @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(305,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) ) )
= $true )
| ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(306,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( SV14 @ ( sK18_Xx @ SV14 ) )
= $true )
| ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(307,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) ) )
= $false )
| ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(308,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK18_Xx @ SV14 ) ) )
= $false )
| ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(309,plain,
! [SV18: $i,SV51: $i,SV58: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ SV58 @ SV51 )
| ~ ( in @ SV58 @ SV18 ) )
= $true )
| ( ( in @ SV51 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(310,plain,
! [SV9: $i > $i > $o,SV18: $i,SV52: $i] :
( ( ( in @ SV52 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( ~ ( ~ ( SV9 @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV52 )
| ~ ( in @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(311,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(312,plain,
! [SV9: $i > $i > $o,SV18: $i,SV41: $i] :
( ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( ~ ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(313,plain,
! [SV11: $i,SV36: $i,SV53: $i] :
( ( ( in @ SV53 @ SV36 )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(314,plain,
! [SV11: $i,SV36: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV36 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(315,plain,
! [SV49: $i,SV11: $i,SV45: $i] :
( ( ( in @ SV45 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( ~ ( in @ SV49 @ ( sK12_B @ SV11 ) ) )
= $true )
| ( ( ! [SY262: $i] :
( ~ ( in @ SY262 @ SV45 )
| ( in @ SY262 @ SV49 ) )
| ! [SY263: $i] :
( ~ ( in @ SY263 @ SV49 )
| ( in @ SY263 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(316,plain,
! [SV11: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ ( sK12_B @ SV11 ) ) )
= $true )
| ( ( ! [SY265: $i] :
( ~ ( in @ SY265 @ SV54 )
| ( in @ SY265 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(317,plain,
! [SV60: $i,SV11: $i,SV55: $i] :
( ( ~ ( in @ SV55 @ SV11 )
| ~ ( in @ SV60 @ SV11 )
| ~ ( ~ ( in @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) ) )
| ( SV55 = SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(318,plain,
! [SV12: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ omega ) )
= $true )
| ( ( in @ SV56 @ SV12 )
= $true )
| ( ( in @ ( sK6_Xx @ SV12 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(319,plain,
! [SV12: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ omega ) )
= $true )
| ( ( in @ SV57 @ SV12 )
= $true )
| ( ( in @ ( sK6_Xx @ SV12 ) @ SV12 )
= $true )
| ( ( in @ emptyset @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(320,plain,
! [SV28: $i,SV61: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ SV61 )
| ( ( sK18_Xx @ SV14 )
= SV61 ) )
= $true )
| ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(321,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( ! [SY227: $i] :
( ~ ( SV14 @ SY227 )
| ( ( sK18_Xx @ SV14 )
= SY227 ) ) )
= $true )
| ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(322,plain,
! [SV28: $i,SV14: $i > $o] :
( ( ( SV14 @ ( sK18_Xx @ SV14 ) )
= $true )
| ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(323,plain,
! [SV18: $i,SV51: $i,SV58: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ SV58 @ SV51 ) )
= $true )
| ( ( ~ ( in @ SV58 @ SV18 ) )
= $true )
| ( ( in @ SV51 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(324,plain,
! [SV18: $i,SV52: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV52 )
| ~ ( in @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( in @ SV52 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(325,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(326,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( ~ ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(327,plain,
! [SV53: $i,SV36: $i,SV11: $i] :
( ( ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(328,plain,
! [SV11: $i,SV36: $i,SV59: $i] :
( ( ( in @ SV59 @ SV36 )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(329,plain,
! [SV45: $i,SV11: $i,SV49: $i] :
( ( ( in @ SV49 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ SV45 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( ! [SY262: $i] :
( ~ ( in @ SY262 @ SV45 )
| ( in @ SY262 @ SV49 ) )
| ! [SY263: $i] :
( ~ ( in @ SY263 @ SV49 )
| ( in @ SY263 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(330,plain,
! [SV11: $i,SV54: $i] :
( ( ( in @ SV54 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( ! [SY265: $i] :
( ~ ( in @ SY265 @ SV54 )
| ( in @ SY265 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(331,plain,
! [SV60: $i,SV11: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV11 )
| ~ ( in @ SV60 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) ) )
| ( SV55 = SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(332,plain,
! [SV12: $i,SV56: $i] :
( ( ( in @ SV56 @ omega )
= $false )
| ( ( in @ SV56 @ SV12 )
= $true )
| ( ( in @ ( sK6_Xx @ SV12 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(333,plain,
! [SV12: $i,SV57: $i] :
( ( ( in @ SV57 @ omega )
= $false )
| ( ( in @ SV57 @ SV12 )
= $true )
| ( ( in @ ( sK6_Xx @ SV12 ) @ SV12 )
= $true )
| ( ( in @ emptyset @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(334,plain,
! [SV28: $i,SV61: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ SV61 ) )
= $true )
| ( ( ( sK18_Xx @ SV14 )
= SV61 )
= $true )
| ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(335,plain,
! [SV28: $i,SV62: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ SV62 )
| ( ( sK18_Xx @ SV14 )
= SV62 ) )
= $true )
| ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(336,plain,
! [SV18: $i,SV51: $i,SV58: $i,SV9: $i > $i > $o] :
( ( ( SV9 @ SV58 @ SV51 )
= $false )
| ( ( ~ ( in @ SV58 @ SV18 ) )
= $true )
| ( ( in @ SV51 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(337,plain,
! [SV18: $i,SV52: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV52 ) )
= $false )
| ( ( in @ SV52 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(338,plain,
! [SV9: $i > $i > $o,SV18: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( in @ SV52 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(339,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(340,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i] :
( ( ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(341,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) )
| ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) )
= $false )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(342,plain,
! [SV53: $i,SV36: $i,SV11: $i] :
( ( ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(343,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(344,plain,
! [SV59: $i,SV36: $i,SV11: $i] :
( ( ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(345,plain,
! [SV11: $i,SV49: $i,SV45: $i] :
( ( ( ! [SY262: $i] :
( ~ ( in @ SY262 @ SV45 )
| ( in @ SY262 @ SV49 ) ) )
= $true )
| ( ( ! [SY263: $i] :
( ~ ( in @ SY263 @ SV49 )
| ( in @ SY263 @ SV45 ) ) )
= $true )
| ( ( in @ SV45 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ SV49 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(346,plain,
! [SV11: $i,SV54: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV54 )
| ( in @ SV63 @ SV11 ) )
= $true )
| ( ( in @ SV54 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(347,plain,
! [SV60: $i,SV11: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV60 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) ) )
| ( SV55 = SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(348,plain,
! [SV28: $i,SV61: $i,SV14: $i > $o] :
( ( ( SV14 @ SV61 )
= $false )
| ( ( ( sK18_Xx @ SV14 )
= SV61 )
= $true )
| ( ( SV14 @ ( sK19_SY71 @ SV28 @ SV14 ) )
= $true )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(349,plain,
! [SV28: $i,SV62: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ SV62 ) )
= $true )
| ( ( ( sK18_Xx @ SV14 )
= SV62 )
= $true )
| ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(350,plain,
! [SV51: $i,SV9: $i > $i > $o,SV18: $i,SV58: $i] :
( ( ( in @ SV58 @ SV18 )
= $false )
| ( ( SV9 @ SV58 @ SV51 )
= $false )
| ( ( in @ SV51 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(351,plain,
! [SV18: $i,SV52: $i,SV9: $i > $i > $o] :
( ( ( SV9 @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV52 )
= $true )
| ( ( in @ SV52 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(352,plain,
! [SV9: $i > $i > $o,SV18: $i,SV52: $i] :
( ( ( in @ ( sK8_Xy @ SV52 @ SV18 @ SV9 ) @ SV18 )
= $true )
| ( ( in @ SV52 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( in @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(353,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(354,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i] :
( ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(355,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ~ ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) ) )
= $false )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(356,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i] :
( ( ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) )
= $false )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(357,plain,
! [SV53: $i,SV36: $i,SV11: $i] :
( ( ( ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(358,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(359,plain,
! [SV59: $i,SV36: $i,SV11: $i] :
( ( ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(360,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(361,plain,
! [SV11: $i,SV49: $i,SV45: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV45 )
| ( in @ SV64 @ SV49 ) )
= $true )
| ( ( ! [SY263: $i] :
( ~ ( in @ SY263 @ SV49 )
| ( in @ SY263 @ SV45 ) ) )
= $true )
| ( ( in @ SV45 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ SV49 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(362,plain,
! [SV11: $i,SV54: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV54 ) )
= $true )
| ( ( in @ SV63 @ SV11 )
= $true )
| ( ( in @ SV54 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(363,plain,
! [SV60: $i,SV11: $i,SV55: $i] :
( ( ( in @ SV55 @ SV11 )
= $false )
| ( ( ~ ( in @ SV60 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) ) )
| ( SV55 = SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(364,plain,
! [SV28: $i,SV62: $i,SV14: $i > $o] :
( ( ( SV14 @ SV62 )
= $false )
| ( ( ( sK18_Xx @ SV14 )
= SV62 )
= $true )
| ( ( SV28
= ( sK19_SY71 @ SV28 @ SV14 ) )
= $false )
| ( ( SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(365,plain,
! [SV41: $i,SV18: $i,SV65: $i,SV9: $i > $i > $o] :
( ( ( ! [SY267: $i] :
( ~ ( SV9 @ SY267 @ SV65 )
| ~ ( in @ SY267 @ SV18 ) )
| ( in @ SV65 @ ( sK7_B @ SV18 @ SV9 ) ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(366,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV66 )
| ~ ( in @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(367,plain,
! [SV41: $i,SV18: $i,SV9: $i > $i > $o] :
( ( ( ! [SY235: $i] :
( ! [SY236: $i] :
( ~ ( SV9 @ SY236 @ SY235 )
| ~ ( in @ SY236 @ SV18 ) )
| ( in @ SY235 @ ( sK7_B @ SV18 @ SV9 ) ) ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(368,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i] :
( ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SY237 )
| ~ ( in @ ( sK8_Xy @ SY237 @ SV18 @ SV9 ) @ SV18 ) ) ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(369,plain,
! [SV53: $i,SV36: $i,SV11: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ ( sK12_B @ SV11 ) )
| ! [SY268: $i] :
( ~ ( in @ SY268 @ SV67 )
| ( in @ SY268 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV67 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(370,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(371,plain,
! [SV59: $i,SV36: $i,SV11: $i] :
( ( ( ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV11 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SY253 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(372,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(373,plain,
! [SV11: $i,SV49: $i,SV45: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV45 ) )
= $true )
| ( ( in @ SV64 @ SV49 )
= $true )
| ( ( ! [SY263: $i] :
( ~ ( in @ SY263 @ SV49 )
| ( in @ SY263 @ SV45 ) ) )
= $true )
| ( ( in @ SV45 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ SV49 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(374,plain,
! [SV11: $i,SV54: $i,SV63: $i] :
( ( ( in @ SV63 @ SV54 )
= $false )
| ( ( in @ SV63 @ SV11 )
= $true )
| ( ( in @ SV54 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(375,plain,
! [SV55: $i,SV11: $i,SV60: $i] :
( ( ( in @ SV60 @ SV11 )
= $false )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) ) )
| ( SV55 = SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(376,plain,
! [SV41: $i,SV18: $i,SV65: $i,SV9: $i > $i > $o] :
( ( ( ! [SY267: $i] :
( ~ ( SV9 @ SY267 @ SV65 )
| ~ ( in @ SY267 @ SV18 ) ) )
= $true )
| ( ( in @ SV65 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(377,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ ( sK7_B @ SV18 @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ( SV9 @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV66 )
| ~ ( in @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(378,plain,
! [SV41: $i,SV18: $i,SV68: $i,SV9: $i > $i > $o] :
( ( ( ! [SY269: $i] :
( ~ ( SV9 @ SY269 @ SV68 )
| ~ ( in @ SY269 @ SV18 ) )
| ( in @ SV68 @ ( sK7_B @ SV18 @ SV9 ) ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(379,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ ( sK7_B @ SV18 @ SV9 ) )
| ~ ( ~ ( SV9 @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV69 )
| ~ ( in @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(380,plain,
! [SV53: $i,SV36: $i,SV11: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ ( sK12_B @ SV11 ) ) )
= $true )
| ( ( ! [SY268: $i] :
( ~ ( in @ SY268 @ SV67 )
| ( in @ SY268 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV67 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(381,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(382,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(383,plain,
! [SV59: $i,SV36: $i,SV11: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ ( sK12_B @ SV11 ) )
| ! [SY270: $i] :
( ~ ( in @ SY270 @ SV70 )
| ( in @ SY270 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV70 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(384,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
| ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(385,plain,
! [SV11: $i,SV49: $i,SV45: $i,SV64: $i] :
( ( ( in @ SV64 @ SV45 )
= $false )
| ( ( in @ SV64 @ SV49 )
= $true )
| ( ( ! [SY263: $i] :
( ~ ( in @ SY263 @ SV49 )
| ( in @ SY263 @ SV45 ) ) )
= $true )
| ( ( in @ SV45 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ SV49 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(386,plain,
! [SV11: $i,SV55: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) ) ) )
= $true )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(387,plain,
! [SV41: $i,SV18: $i,SV65: $i,SV71: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ SV71 @ SV65 )
| ~ ( in @ SV71 @ SV18 ) )
= $true )
| ( ( in @ SV65 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(388,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV66: $i] :
( ( ( in @ SV66 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( ~ ( ~ ( SV9 @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV66 )
| ~ ( in @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(389,plain,
! [SV41: $i,SV18: $i,SV68: $i,SV9: $i > $i > $o] :
( ( ( ! [SY269: $i] :
( ~ ( SV9 @ SY269 @ SV68 )
| ~ ( in @ SY269 @ SV18 ) ) )
= $true )
| ( ( in @ SV68 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(390,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ ( sK7_B @ SV18 @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ( SV9 @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV69 )
| ~ ( in @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(391,plain,
! [SV53: $i,SV36: $i,SV11: $i,SV67: $i] :
( ( ( in @ SV67 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( ! [SY268: $i] :
( ~ ( in @ SY268 @ SV67 )
| ( in @ SY268 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV67 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(392,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(393,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(394,plain,
! [SV59: $i,SV36: $i,SV11: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ ( sK12_B @ SV11 ) ) )
= $true )
| ( ( ! [SY270: $i] :
( ~ ( in @ SY270 @ SV70 )
| ( in @ SY270 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV70 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(395,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(396,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ~ ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(397,plain,
! [SV11: $i,SV64: $i,SV45: $i,SV49: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ SV49 )
| ( in @ SV72 @ SV45 ) )
= $true )
| ( ( in @ SV64 @ SV49 )
= $true )
| ( ( in @ SV64 @ SV45 )
= $false )
| ( ( in @ SV45 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ SV49 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(398,plain,
! [SV11: $i,SV55: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) ) )
= $false )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(399,plain,
! [SV41: $i,SV18: $i,SV65: $i,SV71: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ SV71 @ SV65 ) )
= $true )
| ( ( ~ ( in @ SV71 @ SV18 ) )
= $true )
| ( ( in @ SV65 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(400,plain,
! [SV41: $i,SV18: $i,SV66: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV66 )
| ~ ( in @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( in @ SV66 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(401,plain,
! [SV41: $i,SV18: $i,SV68: $i,SV73: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ SV73 @ SV68 )
| ~ ( in @ SV73 @ SV18 ) )
= $true )
| ( ( in @ SV68 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(402,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV69: $i] :
( ( ( in @ SV69 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( ~ ( ~ ( SV9 @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV69 )
| ~ ( in @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(403,plain,
! [SV53: $i,SV11: $i,SV36: $i,SV67: $i] :
( ( ( ! [SY268: $i] :
( ~ ( in @ SY268 @ SV67 )
| ( in @ SY268 @ ( sK14_SY163 @ SV36 @ SV11 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV67 )
= $true )
| ( ( in @ SV67 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(404,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(405,plain,
! [SV53: $i,SV11: $i,SV36: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SV74 @ SV36 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(406,plain,
! [SV59: $i,SV36: $i,SV11: $i,SV70: $i] :
( ( ( in @ SV70 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( ! [SY270: $i] :
( ~ ( in @ SY270 @ SV70 )
| ( in @ SY270 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
| ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV70 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(407,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(408,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ! [SY255: $i] :
( ~ ( in @ SY255 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SY255 @ SV36 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(409,plain,
! [SV11: $i,SV64: $i,SV45: $i,SV49: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ SV49 ) )
= $true )
| ( ( in @ SV72 @ SV45 )
= $true )
| ( ( in @ SV64 @ SV49 )
= $true )
| ( ( in @ SV64 @ SV45 )
= $false )
| ( ( in @ SV45 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ SV49 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(410,plain,
! [SV11: $i,SV55: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) ) )
= $false )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(411,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) ) )
= $false )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(412,plain,
! [SV41: $i,SV18: $i,SV65: $i,SV71: $i,SV9: $i > $i > $o] :
( ( ( SV9 @ SV71 @ SV65 )
= $false )
| ( ( ~ ( in @ SV71 @ SV18 ) )
= $true )
| ( ( in @ SV65 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(413,plain,
! [SV41: $i,SV18: $i,SV66: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV66 ) )
= $false )
| ( ( in @ SV66 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(414,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( in @ SV66 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(415,plain,
! [SV41: $i,SV18: $i,SV68: $i,SV73: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ SV73 @ SV68 ) )
= $true )
| ( ( ~ ( in @ SV73 @ SV18 ) )
= $true )
| ( ( in @ SV68 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(416,plain,
! [SV41: $i,SV18: $i,SV69: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV69 )
| ~ ( in @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( in @ SV69 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(417,plain,
! [SV53: $i,SV11: $i,SV36: $i,SV67: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV67 )
| ( in @ SV75 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
= $true )
| ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV67 )
= $true )
| ( ( in @ SV67 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(418,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(419,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(420,plain,
! [SV53: $i,SV11: $i,SV36: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
= $true )
| ( ( ~ ( in @ SV74 @ SV36 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(421,plain,
! [SV59: $i,SV11: $i,SV36: $i,SV70: $i] :
( ( ( ! [SY270: $i] :
( ~ ( in @ SY270 @ SV70 )
| ( in @ SY270 @ ( sK14_SY163 @ SV36 @ SV11 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV70 )
= $true )
| ( ( in @ SV70 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(422,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
| ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(423,plain,
! [SV59: $i,SV11: $i,SV36: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( sK14_SY163 @ SV36 @ SV11 ) )
| ~ ( in @ SV76 @ SV36 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(424,plain,
! [SV11: $i,SV64: $i,SV45: $i,SV49: $i,SV72: $i] :
( ( ( in @ SV72 @ SV49 )
= $false )
| ( ( in @ SV72 @ SV45 )
= $true )
| ( ( in @ SV64 @ SV49 )
= $true )
| ( ( in @ SV64 @ SV45 )
= $false )
| ( ( in @ SV45 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ SV49 @ ( sK12_B @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(425,plain,
! [SV11: $i,SV55: $i,SV60: $i] :
( ( ( in @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) @ ( sK12_B @ SV11 ) )
= $true )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(426,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) ) )
= $true )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(427,plain,
! [SV41: $i,SV65: $i,SV9: $i > $i > $o,SV18: $i,SV71: $i] :
( ( ( in @ SV71 @ SV18 )
= $false )
| ( ( SV9 @ SV71 @ SV65 )
= $false )
| ( ( in @ SV65 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(428,plain,
! [SV41: $i,SV18: $i,SV66: $i,SV9: $i > $i > $o] :
( ( ( SV9 @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV66 )
= $true )
| ( ( in @ SV66 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(429,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV66: $i] :
( ( ( in @ ( sK8_Xy @ SV66 @ SV18 @ SV9 ) @ SV18 )
= $true )
| ( ( in @ SV66 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(430,plain,
! [SV41: $i,SV18: $i,SV68: $i,SV73: $i,SV9: $i > $i > $o] :
( ( ( SV9 @ SV73 @ SV68 )
= $false )
| ( ( ~ ( in @ SV73 @ SV18 ) )
= $true )
| ( ( in @ SV68 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(431,plain,
! [SV41: $i,SV18: $i,SV69: $i,SV9: $i > $i > $o] :
( ( ( ~ ( SV9 @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV69 ) )
= $false )
| ( ( in @ SV69 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(432,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( in @ SV69 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(433,plain,
! [SV53: $i,SV11: $i,SV36: $i,SV67: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV67 ) )
= $true )
| ( ( in @ SV75 @ ( sK14_SY163 @ SV36 @ SV11 ) )
= $true )
| ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV67 )
= $true )
| ( ( in @ SV67 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(434,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(435,plain,
! [SV53: $i,SV11: $i,SV36: $i] :
( ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(436,plain,
! [SV53: $i,SV11: $i,SV36: $i,SV74: $i] :
( ( ( in @ SV74 @ ( sK14_SY163 @ SV36 @ SV11 ) )
= $false )
| ( ( ~ ( in @ SV74 @ SV36 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(437,plain,
! [SV59: $i,SV11: $i,SV36: $i,SV70: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ SV70 )
| ( in @ SV77 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
= $true )
| ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV70 )
= $true )
| ( ( in @ SV70 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(438,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(439,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(440,plain,
! [SV59: $i,SV11: $i,SV36: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( sK14_SY163 @ SV36 @ SV11 ) ) )
= $true )
| ( ( ~ ( in @ SV76 @ SV36 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(441,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
| ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) )
= $false )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(442,plain,
! [SV41: $i,SV68: $i,SV9: $i > $i > $o,SV18: $i,SV73: $i] :
( ( ( in @ SV73 @ SV18 )
= $false )
| ( ( SV9 @ SV73 @ SV68 )
= $false )
| ( ( in @ SV68 @ ( sK7_B @ SV18 @ SV9 ) )
= $true )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(443,plain,
! [SV41: $i,SV18: $i,SV69: $i,SV9: $i > $i > $o] :
( ( ( SV9 @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV69 )
= $true )
| ( ( in @ SV69 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(444,plain,
! [SV41: $i,SV9: $i > $i > $o,SV18: $i,SV69: $i] :
( ( ( in @ ( sK8_Xy @ SV69 @ SV18 @ SV9 ) @ SV18 )
= $true )
| ( ( in @ SV69 @ ( sK7_B @ SV18 @ SV9 ) )
= $false )
| ( ( SV41
= ( sK10_SY158 @ SV41 @ SV18 @ SV9 ) )
= $false )
| ( ( SV9 @ ( sK9_SY21 @ SV18 @ SV9 ) @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(445,plain,
! [SV53: $i,SV11: $i,SV36: $i,SV67: $i,SV75: $i] :
( ( ( in @ SV75 @ SV67 )
= $false )
| ( ( in @ SV75 @ ( sK14_SY163 @ SV36 @ SV11 ) )
= $true )
| ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV67 )
= $true )
| ( ( in @ SV67 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(446,plain,
! [SV53: $i,SV11: $i,SV36: $i,SV74: $i] :
( ( ( in @ SV74 @ SV36 )
= $false )
| ( ( in @ SV74 @ ( sK14_SY163 @ SV36 @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ SV53 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(447,plain,
! [SV59: $i,SV11: $i,SV36: $i,SV70: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ SV70 ) )
= $true )
| ( ( in @ SV77 @ ( sK14_SY163 @ SV36 @ SV11 ) )
= $true )
| ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV70 )
= $true )
| ( ( in @ SV70 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(448,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( in @ ( sK14_SY163 @ SV36 @ SV11 ) @ ( sK12_B @ SV11 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(449,plain,
! [SV59: $i,SV11: $i,SV36: $i] :
( ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV36 )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(450,plain,
! [SV59: $i,SV11: $i,SV36: $i,SV76: $i] :
( ( ( in @ SV76 @ ( sK14_SY163 @ SV36 @ SV11 ) )
= $false )
| ( ( ~ ( in @ SV76 @ SV36 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(451,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) )
= $false )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(452,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( ~ ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) ) )
= $false )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(453,plain,
! [SV59: $i,SV11: $i,SV36: $i,SV70: $i,SV77: $i] :
( ( ( in @ SV77 @ SV70 )
= $false )
| ( ( in @ SV77 @ ( sK14_SY163 @ SV36 @ SV11 ) )
= $true )
| ( ( in @ ( sK15_SY177 @ SV36 @ SV11 ) @ SV70 )
= $true )
| ( ( in @ SV70 @ ( sK12_B @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(454,plain,
! [SV59: $i,SV11: $i,SV36: $i,SV76: $i] :
( ( ( in @ SV76 @ SV36 )
= $false )
| ( ( in @ SV76 @ ( sK14_SY163 @ SV36 @ SV11 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV36 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV59 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(455,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
= $true )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(456,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
| ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
= $true )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(457,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
= $true )
| ( ( ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
= $true )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(458,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
= $true )
| ( ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
= $true )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(459,plain,
! [SV11: $i,SV60: $i,SV55: $i] :
( ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
= $false )
| ( ( ~ ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) ) )
= $true )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(460,plain,
! [SV11: $i,SV55: $i,SV60: $i] :
( ( ( in @ SV60 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
= $false )
| ( ( in @ SV55 @ ( sK13_SY176 @ SV60 @ SV55 @ SV11 ) )
= $false )
| ( ( SV55 = SV60 )
= $true )
| ( ( in @ SV55 @ SV11 )
= $false )
| ( ( in @ SV60 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(461,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,460,458,454,453,449,448,446,445,444,443,442,435,434,429,428,427,425,424,374,364,352,351,350,348,333,332,322,306,304,296,295,290,286,285,269,268,267,262,261,250,246,222,214,199,196,154,153,148,134,133,132,126,115,94]) ).
thf(462,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU501^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:26:24 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.62/0.35
% 0.62/0.35 No.of.Axioms: 0
% 0.62/0.35
% 0.62/0.35 Length.of.Defs: 4345
% 0.62/0.35
% 0.62/0.35 Contains.Choice.Funs: true
% 0.62/0.35 ...................
% 0.62/0.35
% 0.62/0.35 ********************************
% 0.62/0.35 * All subproblems solved! *
% 0.62/0.35 ********************************
% 0.62/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:17,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:461,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.62/0.35
% 0.62/0.35 %**** Beginning of derivation protocol ****
% 0.62/0.35 % SZS output start CNFRefutation
% See solution above
% 0.62/0.36
% 0.62/0.36 %**** End of derivation protocol ****
% 0.62/0.36 %**** no. of clauses in derivation: 462 ****
% 0.62/0.36 %**** clause counter: 461 ****
% 0.62/0.36
% 0.62/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:17,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:461,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------