%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU505^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 10:44:39 AM UTC 2026
% Result : Theorem 7.87s 1.55s
% Output : CNFRefutation 7.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 24
% Syntax : Number of formulae : 530 ( 201 unt; 0 typ; 23 def)
% Number of atoms : 4555 (1413 equ; 0 cnn)
% Maximal formula atoms : 26 ( 8 avg)
% Number of connectives : 11303 (1900 ~;1743 |; 118 &;7336 @)
% ( 18 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 265 ( 265 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 27 con; 0-3 aty)
% Number of variables : 1928 ( 73 ^;1807 !; 48 ?;1928 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_exuE3e,type,
exuE3e: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK10_SY186,type,
sK10_SY186: $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_SY204,type,
sK13_SY204: $i > $i > $i > $i ).
thf(tp_sK14_SY191,type,
sK14_SY191: $i > $i > $i ).
thf(tp_sK15_SY205,type,
sK15_SY205: $i > $i > $i ).
thf(tp_sK16_Xx,type,
sK16_Xx: $i > $i > $i ).
thf(tp_sK17_SY56,type,
sK17_SY56: $i > ( $i > $o ) > $i ).
thf(tp_sK18_Xx,type,
sK18_Xx: ( $i > $o ) > $i ).
thf(tp_sK19_SY73,type,
sK19_SY73: $i > ( $i > $o ) > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_Xx,type,
sK20_Xx: ( $i > $o ) > $i ).
thf(tp_sK21_SY86,type,
sK21_SY86: $i > ( $i > $o ) > $i ).
thf(tp_sK2_SY176,type,
sK2_SY176: $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_SY23,type,
sK9_SY23: $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/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(prop2set,definition,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(2,negated_conjecture,
( ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
=> ( ! [SY21: $i > $i > $o,SY22: $i] :
( ! [SY23: $i] :
( ( in @ SY23 @ SY22 )
=> ? [SY25: $i] :
( ( SY21 @ SY23 @ SY25 )
& ! [SY26: $i] :
( ( SY21 @ SY23 @ SY26 )
=> ( SY25 = SY26 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY22 )
& ( SY21 @ 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 ) ) ) ) ) )
=> ( ! [SY53: $i > $o] :
( ? [SY55: $i] :
( ( SY53 @ SY55 )
& ! [SY56: $i] :
( ( SY53 @ SY56 )
=> ( SY55 = SY56 ) ) )
=> ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ 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 ) )
=> ( ! [SY70: $i > $o] :
( ? [SY72: $i] :
( ( SY70 @ SY72 )
& ! [SY73: $i] :
( ( SY70 @ SY73 )
=> ( SY72 = SY73 ) ) )
=> ? [Xx: $i] :
( ( SY70 @ Xx )
& ! [Xy: $i] :
( ( SY70 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY76: $o,SY77: $i] :
( ( in @ SY77
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY78: $i] : SY76 ) )
=> SY76 )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) )
=> ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,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,
( ( ! [SY21: $i > $i > $o,SY22: $i] :
( ! [SY23: $i] :
( ( in @ SY23 @ SY22 )
=> ? [SY25: $i] :
( ( SY21 @ SY23 @ SY25 )
& ! [SY26: $i] :
( ( SY21 @ SY23 @ SY26 )
=> ( SY25 = SY26 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY22 )
& ( SY21 @ 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,
( ( ! [SY53: $i > $o] :
( ? [SY55: $i] :
( ( SY53 @ SY55 )
& ! [SY56: $i] :
( ( SY53 @ SY56 )
=> ( SY55 = SY56 ) ) )
=> ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ 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,
( ( ! [SY70: $i > $o] :
( ? [SY72: $i] :
( ( SY70 @ SY72 )
& ! [SY73: $i] :
( ( SY70 @ SY73 )
=> ( SY72 = SY73 ) ) )
=> ? [Xx: $i] :
( ( SY70 @ Xx )
& ! [Xy: $i] :
( ( SY70 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [SY76: $o,SY77: $i] :
( ( in @ SY77
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY78: $i] : SY76 ) )
=> SY76 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ~ ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [SY179: $i] :
( ~ ( in @ SY179 @ sK1_A )
| ( in @ SY179 @ sK2_SY176 ) )
& ! [SY180: $i] :
( ~ ( in @ SY180 @ sK2_SY176 )
| ( in @ SY180 @ sK1_A ) )
& ( sK1_A != sK2_SY176 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(28,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(29,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(30,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(31,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(32,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(33,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(34,plain,
( ( ! [SY21: $i > $i > $o,SY22: $i] :
( ( ( in @ ( sK9_SY23 @ SY22 @ SY21 ) @ SY22 )
& ! [SY185: $i] :
( ( ( SY21 @ ( sK9_SY23 @ SY22 @ SY21 ) @ ( sK10_SY186 @ SY185 @ SY22 @ SY21 ) )
& ( SY185
!= ( sK10_SY186 @ SY185 @ SY22 @ SY21 ) ) )
| ~ ( SY21 @ ( sK9_SY23 @ SY22 @ SY21 ) @ SY185 ) ) )
| ( ! [SY181: $i] :
( ! [Xy: $i] :
( ~ ( SY21 @ Xy @ SY181 )
| ~ ( in @ Xy @ SY22 ) )
| ( in @ SY181 @ ( sK7_B @ SY22 @ SY21 ) ) )
& ! [SY183: $i] :
( ~ ( in @ SY183 @ ( sK7_B @ SY22 @ SY21 ) )
| ( ( SY21 @ ( sK8_Xy @ SY183 @ SY22 @ SY21 ) @ SY183 )
& ( in @ ( sK8_Xy @ SY183 @ SY22 @ SY21 ) @ SY22 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(35,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK11_B @ A ) @ A )
& ! [SY187: $i] :
( ~ ( in @ SY187 @ ( sK11_B @ A ) )
| ~ ( in @ SY187 @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(36,plain,
( ( ! [A: $i] :
( ! [SY188: $i] :
( ( ( in @ ( sK16_Xx @ SY188 @ A ) @ SY188 )
& ~ ( in @ ( sK16_Xx @ SY188 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY188 )
| ( ! [SY209: $i] :
( ~ ( in @ SY209 @ ( sK12_B @ A ) )
| ! [SY207: $i] :
( ~ ( in @ SY207 @ SY209 )
| ( in @ SY207 @ ( sK14_SY191 @ SY188 @ A ) ) )
| ( in @ ( sK15_SY205 @ SY188 @ A ) @ SY209 ) )
& ( in @ ( sK14_SY191 @ SY188 @ A ) @ ( sK12_B @ A ) )
& ( in @ ( sK15_SY205 @ SY188 @ A ) @ SY188 )
& ! [SY208: $i] :
( ~ ( in @ SY208 @ ( sK14_SY191 @ SY188 @ A ) )
| ~ ( in @ SY208 @ SY188 ) ) ) )
& ! [SY196: $i,SY197: $i] :
( ~ ( in @ SY196 @ ( sK12_B @ A ) )
| ~ ( in @ SY197 @ ( sK12_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY196 )
| ( in @ Xx @ SY197 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY197 )
| ( in @ Xx @ SY196 ) ) )
& ! [SY200: $i] :
( ~ ( in @ SY200 @ ( sK12_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY200 )
| ( in @ Xx @ A ) ) )
& ! [SY202: $i,SY203: $i] :
( ~ ( in @ SY202 @ A )
| ~ ( in @ SY203 @ A )
| ( ( in @ ( sK13_SY204 @ SY203 @ SY202 @ A ) @ ( sK12_B @ A ) )
& ( ~ ( in @ SY202 @ ( sK13_SY204 @ SY203 @ SY202 @ A ) )
| ~ ( in @ SY203 @ ( sK13_SY204 @ SY203 @ SY202 @ A ) ) )
& ( ( in @ SY202 @ ( sK13_SY204 @ SY203 @ SY202 @ A ) )
| ( in @ SY203 @ ( sK13_SY204 @ SY203 @ SY202 @ A ) ) ) )
| ( SY202 = SY203 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(37,plain,
( ( ! [SY53: $i > $o] :
( ! [SY55: $i] :
( ( ( SY53 @ ( sK17_SY56 @ SY55 @ SY53 ) )
& ( SY55
!= ( sK17_SY56 @ SY55 @ SY53 ) ) )
| ~ ( SY53 @ SY55 ) )
| ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(38,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(39,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(40,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(41,plain,
( ( ! [SY70: $i > $o] :
( ! [SY72: $i] :
( ( ( SY70 @ ( sK19_SY73 @ SY72 @ SY70 ) )
& ( SY72
!= ( sK19_SY73 @ SY72 @ SY70 ) ) )
| ~ ( SY70 @ SY72 ) )
| ( ! [SY212: $i] :
( ~ ( SY70 @ SY212 )
| ( ( sK18_Xx @ SY70 )
= SY212 ) )
& ( SY70 @ ( sK18_Xx @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(42,plain,
( ( ! [SY76: $o] :
( ! [SY77: $i] :
~ ( in @ SY77
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY78: $i] : SY76 ) )
| SY76 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(43,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(44,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(45,plain,
( ( ! [SY83: $i > $o] :
( ! [SY85: $i] :
( ( ( SY83 @ ( sK21_SY86 @ SY85 @ SY83 ) )
& ( SY85
!= ( sK21_SY86 @ SY85 @ SY83 ) ) )
| ~ ( SY83 @ SY85 ) )
| ( SY83 @ ( sK20_Xx @ SY83 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(46,plain,
( ( ! [SY83: $i > $o] :
( ! [SY85: $i] :
( ( ( SY83 @ ( sK21_SY86 @ SY85 @ SY83 ) )
& ( SY85
!= ( sK21_SY86 @ SY85 @ SY83 ) ) )
| ~ ( SY83 @ SY85 ) )
| ( SY83 @ ( sK20_Xx @ SY83 ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(48,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(49,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [SY76: $o] :
( ! [SY77: $i] :
~ ( in @ SY77
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY78: $i] : SY76 ) )
| SY76 ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(51,plain,
( ( ! [SY70: $i > $o] :
( ! [SY72: $i] :
( ( ( SY70 @ ( sK19_SY73 @ SY72 @ SY70 ) )
& ( SY72
!= ( sK19_SY73 @ SY72 @ SY70 ) ) )
| ~ ( SY70 @ SY72 ) )
| ( ! [SY212: $i] :
( ~ ( SY70 @ SY212 )
| ( ( sK18_Xx @ SY70 )
= SY212 ) )
& ( SY70 @ ( sK18_Xx @ SY70 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(52,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(53,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(54,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)],[38]) ).
thf(55,plain,
( ( ! [SY53: $i > $o] :
( ! [SY55: $i] :
( ( ( SY53 @ ( sK17_SY56 @ SY55 @ SY53 ) )
& ( SY55
!= ( sK17_SY56 @ SY55 @ SY53 ) ) )
| ~ ( SY53 @ SY55 ) )
| ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(56,plain,
( ( ! [A: $i] :
( ! [SY188: $i] :
( ( ( in @ ( sK16_Xx @ SY188 @ A ) @ SY188 )
& ~ ( in @ ( sK16_Xx @ SY188 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY188 )
| ( ! [SY209: $i] :
( ~ ( in @ SY209 @ ( sK12_B @ A ) )
| ! [SY207: $i] :
( ~ ( in @ SY207 @ SY209 )
| ( in @ SY207 @ ( sK14_SY191 @ SY188 @ A ) ) )
| ( in @ ( sK15_SY205 @ SY188 @ A ) @ SY209 ) )
& ( in @ ( sK14_SY191 @ SY188 @ A ) @ ( sK12_B @ A ) )
& ( in @ ( sK15_SY205 @ SY188 @ A ) @ SY188 )
& ! [SY208: $i] :
( ~ ( in @ SY208 @ ( sK14_SY191 @ SY188 @ A ) )
| ~ ( in @ SY208 @ SY188 ) ) ) )
& ! [SY196: $i,SY197: $i] :
( ~ ( in @ SY196 @ ( sK12_B @ A ) )
| ~ ( in @ SY197 @ ( sK12_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY196 )
| ( in @ Xx @ SY197 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY197 )
| ( in @ Xx @ SY196 ) ) )
& ! [SY200: $i] :
( ~ ( in @ SY200 @ ( sK12_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY200 )
| ( in @ Xx @ A ) ) )
& ! [SY202: $i,SY203: $i] :
( ~ ( in @ SY202 @ A )
| ~ ( in @ SY203 @ A )
| ( ( in @ ( sK13_SY204 @ SY203 @ SY202 @ A ) @ ( sK12_B @ A ) )
& ( ~ ( in @ SY202 @ ( sK13_SY204 @ SY203 @ SY202 @ A ) )
| ~ ( in @ SY203 @ ( sK13_SY204 @ SY203 @ SY202 @ A ) ) )
& ( ( in @ SY202 @ ( sK13_SY204 @ SY203 @ SY202 @ A ) )
| ( in @ SY203 @ ( sK13_SY204 @ SY203 @ SY202 @ A ) ) ) )
| ( SY202 = SY203 ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(57,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK11_B @ A ) @ A )
& ! [SY187: $i] :
( ~ ( in @ SY187 @ ( sK11_B @ A ) )
| ~ ( in @ SY187 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(58,plain,
( ( ! [SY21: $i > $i > $o,SY22: $i] :
( ( ( in @ ( sK9_SY23 @ SY22 @ SY21 ) @ SY22 )
& ! [SY185: $i] :
( ( ( SY21 @ ( sK9_SY23 @ SY22 @ SY21 ) @ ( sK10_SY186 @ SY185 @ SY22 @ SY21 ) )
& ( SY185
!= ( sK10_SY186 @ SY185 @ SY22 @ SY21 ) ) )
| ~ ( SY21 @ ( sK9_SY23 @ SY22 @ SY21 ) @ SY185 ) ) )
| ( ! [SY181: $i] :
( ! [Xy: $i] :
( ~ ( SY21 @ Xy @ SY181 )
| ~ ( in @ Xy @ SY22 ) )
| ( in @ SY181 @ ( sK7_B @ SY22 @ SY21 ) ) )
& ! [SY183: $i] :
( ~ ( in @ SY183 @ ( sK7_B @ SY22 @ SY21 ) )
| ( ( SY21 @ ( sK8_Xy @ SY183 @ SY22 @ SY21 ) @ SY183 )
& ( in @ ( sK8_Xy @ SY183 @ SY22 @ SY21 ) @ SY22 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(59,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)],[33]) ).
thf(60,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(61,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(62,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)],[31]) ).
thf(63,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)],[30]) ).
thf(64,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)],[29]) ).
thf(65,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(66,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)],[28]) ).
thf(67,plain,
( ( ! [SY179: $i] :
( ~ ( in @ SY179 @ sK1_A )
| ( in @ SY179 @ sK2_SY176 ) )
& ! [SY180: $i] :
( ~ ( in @ SY180 @ sK2_SY176 )
| ( in @ SY180 @ sK1_A ) )
& ( sK1_A != sK2_SY176 ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(68,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)],[66,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(69,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK21_SY86 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK21_SY86 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ ( sK20_Xx @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(70,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)],[64,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(71,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ( ~ ( in @ ( sK9_SY23 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK9_SY23 @ SX1 @ SX0 ) @ ( sK10_SY186 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK10_SY186 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ ( sK9_SY23 @ 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)],[58,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(72,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)],[59,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(73,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK17_SY56 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK17_SY56 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(74,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_A )
| ( in @ SX0 @ sK2_SY176 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY176 )
| ( in @ SX0 @ sK1_A ) )
| ~ ( ( sK1_A != sK2_SY176 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(75,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK19_SY73 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK19_SY73 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK18_Xx @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK18_Xx @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(76,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)],[63,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(77,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)],[57,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(78,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_SY191 @ SX1 @ SX0 ) ) )
| ( in @ ( sK15_SY205 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SX1 @ SX0 ) @ ( sK12_B @ SX0 ) )
| ~ ( in @ ( sK15_SY205 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK14_SY191 @ 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_SY204 @ SX2 @ SX1 @ SX0 ) @ ( sK12_B @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ SX1 @ ( sK13_SY204 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK13_SY204 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( in @ SX1 @ ( sK13_SY204 @ SX2 @ SX1 @ SX0 ) )
| ( in @ SX2 @ ( sK13_SY204 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(79,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)],[62,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,prop2setE,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(80,plain,
! [SV1: $i] :
( ( ~ ( in @ SV1 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(81,plain,
! [SV2: $i] :
( ( ~ ( in @ SV2 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(82,plain,
( ( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(83,plain,
! [SV3: $o] :
( ( ! [SY213: $i] :
~ ( in @ SY213
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY214: $i] : SV3 ) )
| SV3 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[50]) ).
thf(84,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[50]) ).
thf(85,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[50]) ).
thf(86,plain,
! [SV4: $i] :
( ( ! [SY215: $i > $o,SY216: $i] :
( ~ ( in @ SY216
@ ( dsetconstr @ SV4
@ ^ [Xy: $i] : ( SY215 @ Xy ) ) )
| ( SY215 @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(87,plain,
! [SV5: $i] :
( ( ! [SY218: $i > $o,SY219: $i] :
( ~ ( in @ SY219
@ ( dsetconstr @ SV5
@ ^ [Xy: $i] : ( SY218 @ Xy ) ) )
| ( in @ SY219 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(88,plain,
! [SV6: $i] :
( ( ! [SY221: $i > $o,SY222: $i] :
( ~ ( in @ SY222 @ SV6 )
| ~ ( SY221 @ SY222 )
| ( in @ SY222
@ ( dsetconstr @ SV6
@ ^ [Xy: $i] : ( SY221 @ Xy ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(89,plain,
! [SV7: $i] :
( ( ~ ( in @ SV7 @ omega )
| ( in @ ( setadjoin @ SV7 @ SV7 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(90,plain,
! [SV8: $i] :
( ( ~ ( in @ SV8 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(91,plain,
! [SV9: $i] :
( ( ! [SY224: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_Xx @ SY224 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK3_Xx @ SY224 @ SV9 ) @ SY224 ) )
| ~ ( ( in @ ( sK3_Xx @ SY224 @ SV9 ) @ SV9 )
| ( in @ ( sK3_Xx @ SY224 @ SV9 ) @ SY224 ) ) )
| ( SV9 = SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(92,plain,
! [SV10: $i > $o] :
( ( ! [SY225: $i] :
( ~ ( ~ ( SV10 @ ( sK21_SY86 @ SY225 @ SV10 ) )
| ~ ( ( SY225
!= ( sK21_SY86 @ SY225 @ SV10 ) ) ) )
| ~ ( SV10 @ SY225 ) )
| ( SV10 @ ( sK20_Xx @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(93,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY226: $i,SY227: $i] :
( ~ ( in @ SY227 @ ( setadjoin @ SV11 @ SY226 ) )
| ( SY227 = SV11 )
| ( in @ SY227 @ SY226 ) )
| ~ ~ ( ~ ! [SY228: $i,SY229: $i] :
( ( SY229 != SV11 )
| ( in @ SY229 @ ( setadjoin @ SV11 @ SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ( in @ SY231 @ SY230 )
| ( in @ SY231 @ ( setadjoin @ SV11 @ SY230 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(94,plain,
! [SV12: $i > $i > $o] :
( ( ! [SY232: $i] :
( ~ ( ~ ( in @ ( sK9_SY23 @ SY232 @ SV12 ) @ SY232 )
| ~ ! [SY233: $i] :
( ~ ( ~ ( SV12 @ ( sK9_SY23 @ SY232 @ SV12 ) @ ( sK10_SY186 @ SY233 @ SY232 @ SV12 ) )
| ~ ( ( SY233
!= ( sK10_SY186 @ SY233 @ SY232 @ SV12 ) ) ) )
| ~ ( SV12 @ ( sK9_SY23 @ SY232 @ SV12 ) @ SY233 ) ) )
| ~ ( ~ ! [SY234: $i] :
( ! [SY235: $i] :
( ~ ( SV12 @ SY235 @ SY234 )
| ~ ( in @ SY235 @ SY232 ) )
| ( in @ SY234 @ ( sK7_B @ SY232 @ SV12 ) ) )
| ~ ! [SY236: $i] :
( ~ ( in @ SY236 @ ( sK7_B @ SY232 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY236 @ SY232 @ SV12 ) @ SY236 )
| ~ ( in @ ( sK8_Xy @ SY236 @ SY232 @ SV12 ) @ SY232 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(95,plain,
! [SV13: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV13 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV13 ) @ SV13 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 ) )
| ~ ( in @ emptyset @ SV13 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(96,plain,
! [SV14: $i > $o] :
( ( ! [SY238: $i] :
( ~ ( ~ ( SV14 @ ( sK17_SY56 @ SY238 @ SV14 ) )
| ~ ( ( SY238
!= ( sK17_SY56 @ SY238 @ SV14 ) ) ) )
| ~ ( SV14 @ SY238 ) )
| ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(97,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_A )
| ( in @ SX0 @ sK2_SY176 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY176 )
| ( in @ SX0 @ sK1_A ) )
| ~ ( ( sK1_A != sK2_SY176 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(98,plain,
! [SV15: $i > $o] :
( ( ! [SY240: $i] :
( ~ ( ~ ( SV15 @ ( sK19_SY73 @ SY240 @ SV15 ) )
| ~ ( ( SY240
!= ( sK19_SY73 @ SY240 @ SV15 ) ) ) )
| ~ ( SV15 @ SY240 ) )
| ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(99,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)],[76]) ).
thf(100,plain,
! [SV16: $i] :
( ( ! [SY242: $i] :
~ ( in @ SY242 @ SV16 )
| ~ ( ~ ( in @ ( sK11_B @ SV16 ) @ SV16 )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK11_B @ SV16 ) )
| ~ ( in @ SY243 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(101,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY244: $i] :
( ~ ( ~ ( in @ ( sK16_Xx @ SY244 @ SV17 ) @ SY244 )
| ~ ~ ( in @ ( sK16_Xx @ SY244 @ SV17 ) @ SV17 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY244 )
| ~ ( ~ ! [SY246: $i] :
( ~ ( in @ SY246 @ ( sK12_B @ SV17 ) )
| ! [SY247: $i] :
( ~ ( in @ SY247 @ SY246 )
| ( in @ SY247 @ ( sK14_SY191 @ SY244 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SY244 @ SV17 ) @ SY246 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SY244 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SY244 @ SV17 ) @ SY244 ) )
| ~ ! [SY248: $i] :
( ~ ( in @ SY248 @ ( sK14_SY191 @ SY244 @ SV17 ) )
| ~ ( in @ SY248 @ SY244 ) ) ) ) )
| ~ ~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SY250 @ ( sK12_B @ SV17 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(102,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)],[79]) ).
thf(103,plain,
! [SV1: $i] :
( ( in @ SV1 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(104,plain,
! [SV2: $i] :
( ( in @ SV2 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(105,plain,
! [SV18: $i] :
( ( ( ~ ( in @ SV18 @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(106,plain,
! [SV3: $o] :
( ( ( ! [SY213: $i] :
~ ( in @ SY213
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY214: $i] : SV3 ) ) )
= $true )
| ( SV3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(107,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(108,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(109,plain,
! [SV19: $i > $o,SV4: $i] :
( ( ! [SY257: $i] :
( ~ ( in @ SY257
@ ( dsetconstr @ SV4
@ ^ [SY258: $i] : ( SV19 @ SY258 ) ) )
| ( SV19 @ SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(110,plain,
! [SV20: $i > $o,SV5: $i] :
( ( ! [SY259: $i] :
( ~ ( in @ SY259
@ ( dsetconstr @ SV5
@ ^ [SY260: $i] : ( SV20 @ SY260 ) ) )
| ( in @ SY259 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(111,plain,
! [SV21: $i > $o,SV6: $i] :
( ( ! [SY261: $i] :
( ~ ( in @ SY261 @ SV6 )
| ~ ( SV21 @ SY261 )
| ( in @ SY261
@ ( dsetconstr @ SV6
@ ^ [SY262: $i] : ( SV21 @ SY262 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(112,plain,
! [SV7: $i] :
( ( ( ~ ( in @ SV7 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV7 @ SV7 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(113,plain,
! [SV8: $i] :
( ( in @ SV8 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(114,plain,
! [SV9: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) )
| ~ ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) ) )
| ( SV9 = SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(115,plain,
! [SV10: $i > $o] :
( ( ( ! [SY225: $i] :
( ~ ( ~ ( SV10 @ ( sK21_SY86 @ SY225 @ SV10 ) )
| ~ ( ( SY225
!= ( sK21_SY86 @ SY225 @ SV10 ) ) ) )
| ~ ( SV10 @ SY225 ) ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(116,plain,
! [SV11: $i] :
( ( ~ ! [SY226: $i,SY227: $i] :
( ~ ( in @ SY227 @ ( setadjoin @ SV11 @ SY226 ) )
| ( SY227 = SV11 )
| ( in @ SY227 @ SY226 ) )
| ~ ~ ( ~ ! [SY228: $i,SY229: $i] :
( ( SY229 != SV11 )
| ( in @ SY229 @ ( setadjoin @ SV11 @ SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ( in @ SY231 @ SY230 )
| ( in @ SY231 @ ( setadjoin @ SV11 @ SY230 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(117,plain,
! [SV12: $i > $i > $o,SV23: $i] :
( ( ~ ( ~ ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
| ~ ! [SY263: $i] :
( ~ ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) )
| ~ ( ( SY263
!= ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) ) ) )
| ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SY263 ) ) )
| ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(118,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV13 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV13 ) @ SV13 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 ) )
| ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(119,plain,
! [SV14: $i > $o] :
( ( ( ! [SY238: $i] :
( ~ ( ~ ( SV14 @ ( sK17_SY56 @ SY238 @ SV14 ) )
| ~ ( ( SY238
!= ( sK17_SY56 @ SY238 @ SV14 ) ) ) )
| ~ ( SV14 @ SY238 ) ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(120,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_A )
| ( in @ SX0 @ sK2_SY176 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(121,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY176 )
| ( in @ SX0 @ sK1_A ) )
| ~ ( ( sK1_A != sK2_SY176 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(122,plain,
! [SV15: $i > $o] :
( ( ( ! [SY240: $i] :
( ~ ( ~ ( SV15 @ ( sK19_SY73 @ SY240 @ SV15 ) )
| ~ ( ( SY240
!= ( sK19_SY73 @ SY240 @ SV15 ) ) ) )
| ~ ( SV15 @ SY240 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(123,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)],[99]) ).
thf(124,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(125,plain,
! [SV16: $i] :
( ( ( ! [SY242: $i] :
~ ( in @ SY242 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_B @ SV16 ) @ SV16 )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK11_B @ SV16 ) )
| ~ ( in @ SY243 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(126,plain,
! [SV17: $i] :
( ( ~ ! [SY244: $i] :
( ~ ( ~ ( in @ ( sK16_Xx @ SY244 @ SV17 ) @ SY244 )
| ~ ~ ( in @ ( sK16_Xx @ SY244 @ SV17 ) @ SV17 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY244 )
| ~ ( ~ ! [SY246: $i] :
( ~ ( in @ SY246 @ ( sK12_B @ SV17 ) )
| ! [SY247: $i] :
( ~ ( in @ SY247 @ SY246 )
| ( in @ SY247 @ ( sK14_SY191 @ SY244 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SY244 @ SV17 ) @ SY246 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SY244 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SY244 @ SV17 ) @ SY244 ) )
| ~ ! [SY248: $i] :
( ~ ( in @ SY248 @ ( sK14_SY191 @ SY244 @ SV17 ) )
| ~ ( in @ SY248 @ SY244 ) ) ) ) )
| ~ ~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SY250 @ ( sK12_B @ SV17 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(127,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(128,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)],[102]) ).
thf(129,plain,
! [SV18: $i] :
( ( ( in @ SV18 @ emptyset )
= $false )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(130,plain,
! [SV3: $o,SV24: $i] :
( ( ( ~ ( in @ SV24
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY214: $i] : SV3 ) ) )
= $true )
| ( SV3 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(131,plain,
! [SV25: $i] :
( ( ( ~ ( in @ SV25
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(132,plain,
! [SV26: $i] :
( ( ( ~ ( in @ SV26
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(133,plain,
! [SV19: $i > $o,SV4: $i,SV27: $i] :
( ( ~ ( in @ SV27
@ ( dsetconstr @ SV4
@ ^ [SY258: $i] : ( SV19 @ SY258 ) ) )
| ( SV19 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(134,plain,
! [SV20: $i > $o,SV5: $i,SV28: $i] :
( ( ~ ( in @ SV28
@ ( dsetconstr @ SV5
@ ^ [SY260: $i] : ( SV20 @ SY260 ) ) )
| ( in @ SV28 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(135,plain,
! [SV21: $i > $o,SV6: $i,SV29: $i] :
( ( ~ ( in @ SV29 @ SV6 )
| ~ ( SV21 @ SV29 )
| ( in @ SV29
@ ( dsetconstr @ SV6
@ ^ [SY262: $i] : ( SV21 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(136,plain,
! [SV7: $i] :
( ( ( in @ SV7 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV7 @ SV7 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(137,plain,
! [SV9: $i,SV22: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) )
| ~ ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) ) ) )
= $true )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(138,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK21_SY86 @ SV30 @ SV10 ) )
| ~ ( ( SV30
!= ( sK21_SY86 @ SV30 @ SV10 ) ) ) )
| ~ ( SV10 @ SV30 ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(139,plain,
! [SV11: $i] :
( ( ~ ! [SY226: $i,SY227: $i] :
( ~ ( in @ SY227 @ ( setadjoin @ SV11 @ SY226 ) )
| ( SY227 = SV11 )
| ( in @ SY227 @ SY226 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(140,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ! [SY228: $i,SY229: $i] :
( ( SY229 != SV11 )
| ( in @ SY229 @ ( setadjoin @ SV11 @ SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ( in @ SY231 @ SY230 )
| ( in @ SY231 @ ( setadjoin @ SV11 @ SY230 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(141,plain,
! [SV12: $i > $i > $o,SV23: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
| ~ ! [SY263: $i] :
( ~ ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) )
| ~ ( ( SY263
!= ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) ) ) )
| ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SY263 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(142,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV13 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV13 ) @ SV13 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(143,plain,
! [SV31: $i,SV14: $i > $o] :
( ( ( ~ ( ~ ( SV14 @ ( sK17_SY56 @ SV31 @ SV14 ) )
| ~ ( ( SV31
!= ( sK17_SY56 @ SV31 @ SV14 ) ) ) )
| ~ ( SV14 @ SV31 ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(144,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_A )
| ( in @ SX0 @ sK2_SY176 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(145,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY176 )
| ( in @ SX0 @ sK1_A ) )
| ~ ( ( sK1_A != sK2_SY176 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(146,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
| ~ ( ( SV32
!= ( sK19_SY73 @ SV32 @ SV15 ) ) ) )
| ~ ( SV15 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(147,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)],[123]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(149,plain,
! [SV16: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_B @ SV16 ) @ SV16 )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK11_B @ SV16 ) )
| ~ ( in @ SY243 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(150,plain,
! [SV17: $i] :
( ( ~ ! [SY244: $i] :
( ~ ( ~ ( in @ ( sK16_Xx @ SY244 @ SV17 ) @ SY244 )
| ~ ~ ( in @ ( sK16_Xx @ SY244 @ SV17 ) @ SV17 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY244 )
| ~ ( ~ ! [SY246: $i] :
( ~ ( in @ SY246 @ ( sK12_B @ SV17 ) )
| ! [SY247: $i] :
( ~ ( in @ SY247 @ SY246 )
| ( in @ SY247 @ ( sK14_SY191 @ SY244 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SY244 @ SV17 ) @ SY246 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SY244 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SY244 @ SV17 ) @ SY244 ) )
| ~ ! [SY248: $i] :
( ~ ( in @ SY248 @ ( sK14_SY191 @ SY244 @ SV17 ) )
| ~ ( in @ SY248 @ SY244 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(151,plain,
! [SV17: $i] :
( ( ~ ~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SY250 @ ( sK12_B @ SV17 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(153,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)],[128]) ).
thf(154,plain,
! [SV18: $i,SV34: $o] :
( ( SV34 = $true )
| ( ( in @ SV18 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[129]) ).
thf(155,plain,
! [SV18: $i] :
( ( $true = $true )
| ( ( in @ SV18 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[129]) ).
thf(156,plain,
! [SV18: $i] :
( ( $false = $true )
| ( ( in @ SV18 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[129]) ).
thf(157,plain,
! [SV3: $o,SV24: $i] :
( ( ( in @ SV24
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY214: $i] : SV3 ) )
= $false )
| ( SV3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(158,plain,
! [SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(159,plain,
! [SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(160,plain,
! [SV19: $i > $o,SV4: $i,SV27: $i] :
( ( ( ~ ( in @ SV27
@ ( dsetconstr @ SV4
@ ^ [SY258: $i] : ( SV19 @ SY258 ) ) ) )
= $true )
| ( ( SV19 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(161,plain,
! [SV20: $i > $o,SV5: $i,SV28: $i] :
( ( ( ~ ( in @ SV28
@ ( dsetconstr @ SV5
@ ^ [SY260: $i] : ( SV20 @ SY260 ) ) ) )
= $true )
| ( ( in @ SV28 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(162,plain,
! [SV21: $i > $o,SV6: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV6 ) )
= $true )
| ( ( ~ ( SV21 @ SV29 )
| ( in @ SV29
@ ( dsetconstr @ SV6
@ ^ [SY262: $i] : ( SV21 @ SY262 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(163,plain,
! [SV9: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) )
| ~ ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) ) )
= $false )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(164,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK21_SY86 @ SV30 @ SV10 ) )
| ~ ( ( SV30
!= ( sK21_SY86 @ SV30 @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ( SV10 @ SV30 ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(165,plain,
! [SV11: $i] :
( ( ! [SY226: $i,SY227: $i] :
( ~ ( in @ SY227 @ ( setadjoin @ SV11 @ SY226 ) )
| ( SY227 = SV11 )
| ( in @ SY227 @ SY226 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(166,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY228: $i,SY229: $i] :
( ( SY229 != SV11 )
| ( in @ SY229 @ ( setadjoin @ SV11 @ SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ( in @ SY231 @ SY230 )
| ( in @ SY231 @ ( setadjoin @ SV11 @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(167,plain,
! [SV12: $i > $i > $o,SV23: $i] :
( ( ( ~ ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
| ~ ! [SY263: $i] :
( ~ ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) )
| ~ ( ( SY263
!= ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) ) ) )
| ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SY263 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(168,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV13 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV13 ) @ SV13 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(169,plain,
! [SV31: $i,SV14: $i > $o] :
( ( ( ~ ( ~ ( SV14 @ ( sK17_SY56 @ SV31 @ SV14 ) )
| ~ ( ( SV31
!= ( sK17_SY56 @ SV31 @ SV14 ) ) ) ) )
= $true )
| ( ( ~ ( SV14 @ SV31 ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(170,plain,
! [SV35: $i] :
( ( ~ ( in @ SV35 @ sK1_A )
| ( in @ SV35 @ sK2_SY176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(171,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY176 )
| ( in @ SX0 @ sK1_A ) )
| ~ ( ( sK1_A != sK2_SY176 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(172,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
| ~ ( ( SV32
!= ( sK19_SY73 @ SV32 @ SV15 ) ) ) ) )
= $true )
| ( ( ~ ( SV15 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(173,plain,
! [SV36: $i] :
( ( ! [SY273: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SY273 @ SV36 ) @ SY273 )
| ~ ~ ( in @ ( sK4_Xx @ SY273 @ SV36 ) @ SV36 ) )
| ( in @ SY273 @ ( powerset @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(174,plain,
! [SV37: $i] :
( ( ! [SY274: $i] :
( ~ ( in @ SY274 @ ( powerset @ SV37 ) )
| ! [SY275: $i] :
( ~ ( in @ SY275 @ SY274 )
| ( in @ SY275 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(175,plain,
! [SV16: $i,SV33: $i] :
( ( ( in @ SV33 @ SV16 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_B @ SV16 ) @ SV16 )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK11_B @ SV16 ) )
| ~ ( in @ SY243 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(176,plain,
! [SV17: $i] :
( ( ! [SY244: $i] :
( ~ ( ~ ( in @ ( sK16_Xx @ SY244 @ SV17 ) @ SY244 )
| ~ ~ ( in @ ( sK16_Xx @ SY244 @ SV17 ) @ SV17 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY244 )
| ~ ( ~ ! [SY246: $i] :
( ~ ( in @ SY246 @ ( sK12_B @ SV17 ) )
| ! [SY247: $i] :
( ~ ( in @ SY247 @ SY246 )
| ( in @ SY247 @ ( sK14_SY191 @ SY244 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SY244 @ SV17 ) @ SY246 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SY244 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SY244 @ SV17 ) @ SY244 ) )
| ~ ! [SY248: $i] :
( ~ ( in @ SY248 @ ( sK14_SY191 @ SY244 @ SV17 ) )
| ~ ( in @ SY248 @ SY244 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(177,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SY250 @ ( sK12_B @ SV17 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(178,plain,
! [SV38: $i] :
( ( ! [SY276: $i] :
( ! [SY277: $i] :
( ~ ( in @ SY276 @ SY277 )
| ~ ( in @ SY277 @ SV38 ) )
| ( in @ SY276 @ ( setunion @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(179,plain,
! [SV39: $i] :
( ( ! [SY278: $i] :
( ~ ( in @ SY278 @ ( setunion @ SV39 ) )
| ~ ( ~ ( in @ SY278 @ ( sK5_B @ SY278 @ SV39 ) )
| ~ ( in @ ( sK5_B @ SY278 @ SV39 ) @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(180,plain,
! [SV19: $i > $o,SV4: $i,SV27: $i] :
( ( ( in @ SV27
@ ( dsetconstr @ SV4
@ ^ [SY258: $i] : ( SV19 @ SY258 ) ) )
= $false )
| ( ( SV19 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(181,plain,
! [SV20: $i > $o,SV5: $i,SV28: $i] :
( ( ( in @ SV28
@ ( dsetconstr @ SV5
@ ^ [SY260: $i] : ( SV20 @ SY260 ) ) )
= $false )
| ( ( in @ SV28 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(182,plain,
! [SV21: $i > $o,SV6: $i,SV29: $i] :
( ( ( in @ SV29 @ SV6 )
= $false )
| ( ( ~ ( SV21 @ SV29 )
| ( in @ SV29
@ ( dsetconstr @ SV6
@ ^ [SY262: $i] : ( SV21 @ SY262 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(183,plain,
! [SV9: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) ) )
= $false )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(184,plain,
! [SV9: $i,SV22: $i] :
( ( ( ~ ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) ) )
= $false )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(185,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK21_SY86 @ SV30 @ SV10 ) )
| ~ ( ( SV30
!= ( sK21_SY86 @ SV30 @ SV10 ) ) ) )
= $false )
| ( ( ~ ( SV10 @ SV30 ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(186,plain,
! [SV40: $i,SV11: $i] :
( ( ! [SY279: $i] :
( ~ ( in @ SY279 @ ( setadjoin @ SV11 @ SV40 ) )
| ( SY279 = SV11 )
| ( in @ SY279 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(187,plain,
! [SV11: $i] :
( ( ~ ! [SY228: $i,SY229: $i] :
( ( SY229 != SV11 )
| ( in @ SY229 @ ( setadjoin @ SV11 @ SY228 ) ) )
| ~ ! [SY230: $i,SY231: $i] :
( ~ ( in @ SY231 @ SY230 )
| ( in @ SY231 @ ( setadjoin @ SV11 @ SY230 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(188,plain,
! [SV12: $i > $i > $o,SV23: $i] :
( ( ( ~ ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 ) )
= $false )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(189,plain,
! [SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ! [SY263: $i] :
( ~ ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) )
| ~ ( ( SY263
!= ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) ) ) )
| ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SY263 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(190,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_Xx @ SV13 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV13 ) @ SV13 ) ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(191,plain,
! [SV13: $i] :
( ( ( ~ ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(192,plain,
! [SV31: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK17_SY56 @ SV31 @ SV14 ) )
| ~ ( ( SV31
!= ( sK17_SY56 @ SV31 @ SV14 ) ) ) )
= $false )
| ( ( ~ ( SV14 @ SV31 ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(193,plain,
! [SV35: $i] :
( ( ( ~ ( in @ SV35 @ sK1_A ) )
= $true )
| ( ( in @ SV35 @ sK2_SY176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(194,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY176 )
| ( in @ SX0 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(195,plain,
( ( ~ ( ( sK1_A != sK2_SY176 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(196,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
| ~ ( ( SV32
!= ( sK19_SY73 @ SV32 @ SV15 ) ) ) )
= $false )
| ( ( ~ ( SV15 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(197,plain,
! [SV36: $i,SV41: $i] :
( ( ~ ( ~ ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV41 )
| ~ ~ ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV36 ) )
| ( in @ SV41 @ ( powerset @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(198,plain,
! [SV37: $i,SV42: $i] :
( ( ~ ( in @ SV42 @ ( powerset @ SV37 ) )
| ! [SY280: $i] :
( ~ ( in @ SY280 @ SV42 )
| ( in @ SY280 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(199,plain,
! [SV33: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK11_B @ SV16 ) @ SV16 )
| ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK11_B @ SV16 ) )
| ~ ( in @ SY243 @ SV16 ) ) )
= $false )
| ( ( in @ SV33 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(200,plain,
! [SV17: $i,SV43: $i] :
( ( ~ ( ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
| ~ ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 ) )
| ! [SY281: $i] :
~ ( in @ SY281 @ SV43 )
| ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(201,plain,
! [SV17: $i] :
( ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SY250 @ ( sK12_B @ SV17 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(202,plain,
! [SV38: $i,SV44: $i] :
( ( ! [SY285: $i] :
( ~ ( in @ SV44 @ SY285 )
| ~ ( in @ SY285 @ SV38 ) )
| ( in @ SV44 @ ( setunion @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(203,plain,
! [SV39: $i,SV45: $i] :
( ( ~ ( in @ SV45 @ ( setunion @ SV39 ) )
| ~ ( ~ ( in @ SV45 @ ( sK5_B @ SV45 @ SV39 ) )
| ~ ( in @ ( sK5_B @ SV45 @ SV39 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(204,plain,
! [SV6: $i,SV29: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV29 ) )
= $true )
| ( ( in @ SV29
@ ( dsetconstr @ SV6
@ ^ [SY262: $i] : ( SV21 @ SY262 ) ) )
= $true )
| ( ( in @ SV29 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(205,plain,
! [SV9: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) )
= $true )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(206,plain,
! [SV9: $i,SV22: $i] :
( ( ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
| ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) )
= $true )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(207,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK21_SY86 @ SV30 @ SV10 ) ) )
= $false )
| ( ( ~ ( SV10 @ SV30 ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(208,plain,
! [SV10: $i > $o,SV30: $i] :
( ( ( ~ ( ( SV30
!= ( sK21_SY86 @ SV30 @ SV10 ) ) ) )
= $false )
| ( ( ~ ( SV10 @ SV30 ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(209,plain,
! [SV40: $i,SV11: $i,SV46: $i] :
( ( ~ ( in @ SV46 @ ( setadjoin @ SV11 @ SV40 ) )
| ( SV46 = SV11 )
| ( in @ SV46 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(210,plain,
! [SV11: $i] :
( ( ~ ! [SY228: $i,SY229: $i] :
( ( SY229 != SV11 )
| ( in @ SY229 @ ( setadjoin @ SV11 @ SY228 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(211,plain,
! [SV11: $i] :
( ( ~ ! [SY230: $i,SY231: $i] :
( ~ ( in @ SY231 @ SY230 )
| ( in @ SY231 @ ( setadjoin @ SV11 @ SY230 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(212,plain,
! [SV12: $i > $i > $o,SV23: $i] :
( ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(213,plain,
! [SV23: $i,SV12: $i > $i > $o] :
( ( ( ! [SY263: $i] :
( ~ ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) )
| ~ ( ( SY263
!= ( sK10_SY186 @ SY263 @ SV23 @ SV12 ) ) ) )
| ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SY263 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(214,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_Xx @ SV13 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(215,plain,
! [SV13: $i] :
( ( ( ~ ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(216,plain,
! [SV31: $i,SV14: $i > $o] :
( ( ( ~ ( SV14 @ ( sK17_SY56 @ SV31 @ SV14 ) ) )
= $false )
| ( ( ~ ( SV14 @ SV31 ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(217,plain,
! [SV14: $i > $o,SV31: $i] :
( ( ( ~ ( ( SV31
!= ( sK17_SY56 @ SV31 @ SV14 ) ) ) )
= $false )
| ( ( ~ ( SV14 @ SV31 ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(218,plain,
! [SV35: $i] :
( ( ( in @ SV35 @ sK1_A )
= $false )
| ( ( in @ SV35 @ sK2_SY176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(219,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY176 )
| ( in @ SX0 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(220,plain,
( ( sK1_A != sK2_SY176 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(221,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) ) )
= $false )
| ( ( ~ ( SV15 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(222,plain,
! [SV15: $i > $o,SV32: $i] :
( ( ( ~ ( ( SV32
!= ( sK19_SY73 @ SV32 @ SV15 ) ) ) )
= $false )
| ( ( ~ ( SV15 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(223,plain,
! [SV36: $i,SV41: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV41 )
| ~ ~ ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( in @ SV41 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(224,plain,
! [SV37: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ! [SY280: $i] :
( ~ ( in @ SY280 @ SV42 )
| ( in @ SY280 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(225,plain,
! [SV33: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK11_B @ SV16 ) @ SV16 ) )
= $false )
| ( ( in @ SV33 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(226,plain,
! [SV33: $i,SV16: $i] :
( ( ( ~ ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK11_B @ SV16 ) )
| ~ ( in @ SY243 @ SV16 ) ) )
= $false )
| ( ( in @ SV33 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(227,plain,
! [SV17: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
| ~ ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 ) )
| ! [SY281: $i] :
~ ( in @ SY281 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(228,plain,
! [SV17: $i] :
( ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SY250 @ ( sK12_B @ SV17 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(229,plain,
! [SV17: $i] :
( ( ~ ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(230,plain,
! [SV38: $i,SV44: $i] :
( ( ( ! [SY285: $i] :
( ~ ( in @ SV44 @ SY285 )
| ~ ( in @ SY285 @ SV38 ) ) )
= $true )
| ( ( in @ SV44 @ ( setunion @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(231,plain,
! [SV39: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ ( setunion @ SV39 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV45 @ ( sK5_B @ SV45 @ SV39 ) )
| ~ ( in @ ( sK5_B @ SV45 @ SV39 ) @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(232,plain,
! [SV6: $i,SV29: $i,SV21: $i > $o] :
( ( ( SV21 @ SV29 )
= $false )
| ( ( in @ SV29
@ ( dsetconstr @ SV6
@ ^ [SY262: $i] : ( SV21 @ SY262 ) ) )
= $true )
| ( ( in @ SV29 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(233,plain,
! [SV9: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 ) )
= $true )
| ( ( ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) )
= $true )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(234,plain,
! [SV9: $i,SV22: $i] :
( ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
= $true )
| ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 )
= $true )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(235,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK21_SY86 @ SV30 @ SV10 ) )
= $true )
| ( ( ~ ( SV10 @ SV30 ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(236,plain,
! [SV10: $i > $o,SV30: $i] :
( ( ( SV30
!= ( sK21_SY86 @ SV30 @ SV10 ) )
= $true )
| ( ( ~ ( SV10 @ SV30 ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(237,plain,
! [SV40: $i,SV11: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ ( setadjoin @ SV11 @ SV40 ) ) )
= $true )
| ( ( ( SV46 = SV11 )
| ( in @ SV46 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(238,plain,
! [SV11: $i] :
( ( ! [SY228: $i,SY229: $i] :
( ( SY229 != SV11 )
| ( in @ SY229 @ ( setadjoin @ SV11 @ SY228 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(239,plain,
! [SV11: $i] :
( ( ! [SY230: $i,SY231: $i] :
( ~ ( in @ SY231 @ SY230 )
| ( in @ SY231 @ ( setadjoin @ SV11 @ SY230 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(240,plain,
! [SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(241,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
| ~ ( ( SV47
!= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) ) ) )
| ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(242,plain,
! [SV13: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV13 ) @ omega )
| ~ ( in @ ( sK6_Xx @ SV13 ) @ SV13 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(243,plain,
! [SV13: $i] :
( ( ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 )
= $false )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(244,plain,
! [SV31: $i,SV14: $i > $o] :
( ( ( SV14 @ ( sK17_SY56 @ SV31 @ SV14 ) )
= $true )
| ( ( ~ ( SV14 @ SV31 ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(245,plain,
! [SV14: $i > $o,SV31: $i] :
( ( ( SV31
!= ( sK17_SY56 @ SV31 @ SV14 ) )
= $true )
| ( ( ~ ( SV14 @ SV31 ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(246,plain,
! [SV48: $i] :
( ( ~ ( in @ SV48 @ sK2_SY176 )
| ( in @ SV48 @ sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(247,plain,
( ( sK1_A = sK2_SY176 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(248,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( ~ ( SV15 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(249,plain,
! [SV15: $i > $o,SV32: $i] :
( ( ( SV32
!= ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( ~ ( SV15 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(250,plain,
! [SV36: $i,SV41: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV41 )
| ~ ~ ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV36 ) )
= $false )
| ( ( in @ SV41 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(251,plain,
! [SV37: $i,SV42: $i] :
( ( ( in @ SV42 @ ( powerset @ SV37 ) )
= $false )
| ( ( ! [SY280: $i] :
( ~ ( in @ SY280 @ SV42 )
| ( in @ SY280 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(252,plain,
! [SV33: $i,SV16: $i] :
( ( ( in @ ( sK11_B @ SV16 ) @ SV16 )
= $true )
| ( ( in @ SV33 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(253,plain,
! [SV33: $i,SV16: $i] :
( ( ( ! [SY243: $i] :
( ~ ( in @ SY243 @ ( sK11_B @ SV16 ) )
| ~ ( in @ SY243 @ SV16 ) ) )
= $true )
| ( ( in @ SV33 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(254,plain,
! [SV17: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
| ~ ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 ) ) )
= $true )
| ( ( ! [SY281: $i] :
~ ( in @ SY281 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(255,plain,
! [SV17: $i] :
( ( ! [SY249: $i,SY250: $i] :
( ~ ( in @ SY249 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SY250 @ ( sK12_B @ SV17 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY249 )
| ( in @ SX3 @ SY250 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(256,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(257,plain,
! [SV38: $i,SV49: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV49 )
| ~ ( in @ SV49 @ SV38 ) )
= $true )
| ( ( in @ SV44 @ ( setunion @ SV38 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(258,plain,
! [SV39: $i,SV45: $i] :
( ( ( in @ SV45 @ ( setunion @ SV39 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV45 @ ( sK5_B @ SV45 @ SV39 ) )
| ~ ( in @ ( sK5_B @ SV45 @ SV39 ) @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(259,plain,
! [SV9: $i,SV22: $i] :
( ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
= $false )
| ( ( ~ ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 ) )
= $true )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(260,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK21_SY86 @ SV30 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(261,plain,
! [SV10: $i > $o,SV30: $i] :
( ( ( SV30
= ( sK21_SY86 @ SV30 @ SV10 ) )
= $false )
| ( ( ~ ( SV10 @ SV30 ) )
= $true )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(262,plain,
! [SV40: $i,SV11: $i,SV46: $i] :
( ( ( in @ SV46 @ ( setadjoin @ SV11 @ SV40 ) )
= $false )
| ( ( ( SV46 = SV11 )
| ( in @ SV46 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(263,plain,
! [SV50: $i,SV11: $i] :
( ( ! [SY286: $i] :
( ( SY286 != SV11 )
| ( in @ SY286 @ ( setadjoin @ SV11 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(264,plain,
! [SV11: $i,SV51: $i] :
( ( ! [SY287: $i] :
( ~ ( in @ SY287 @ SV51 )
| ( in @ SY287 @ ( setadjoin @ SV11 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(265,plain,
! [SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(266,plain,
! [SV12: $i > $i > $o,SV23: $i] :
( ( ( ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(267,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
| ~ ( ( SV47
!= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) ) ) ) )
= $true )
| ( ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(268,plain,
! [SV13: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV13 ) @ omega ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(269,plain,
! [SV13: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV13 ) @ SV13 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(270,plain,
! [SV13: $i] :
( ( ( in @ emptyset @ SV13 )
= $false )
| ( ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 )
= $false )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(271,plain,
! [SV31: $i,SV14: $i > $o] :
( ( ( SV14 @ SV31 )
= $false )
| ( ( SV14 @ ( sK17_SY56 @ SV31 @ SV14 ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(272,plain,
! [SV14: $i > $o,SV31: $i] :
( ( ( SV31
= ( sK17_SY56 @ SV31 @ SV14 ) )
= $false )
| ( ( ~ ( SV14 @ SV31 ) )
= $true )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(273,plain,
! [SV48: $i] :
( ( ( ~ ( in @ SV48 @ sK2_SY176 ) )
= $true )
| ( ( in @ SV48 @ sK1_A )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(274,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( SV15 @ SV32 )
= $false )
| ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(275,plain,
! [SV15: $i > $o,SV32: $i] :
( ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( ~ ( SV15 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(276,plain,
! [SV36: $i,SV41: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV41 ) )
= $false )
| ( ( in @ SV41 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(277,plain,
! [SV36: $i,SV41: $i] :
( ( ( ~ ~ ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV36 ) )
= $false )
| ( ( in @ SV41 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(278,plain,
! [SV37: $i,SV42: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV42 )
| ( in @ SV52 @ SV37 ) )
= $true )
| ( ( in @ SV42 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(279,plain,
! [SV33: $i,SV16: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ ( sK11_B @ SV16 ) )
| ~ ( in @ SV53 @ SV16 ) )
= $true )
| ( ( in @ SV33 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(280,plain,
! [SV17: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
| ~ ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 ) )
= $false )
| ( ( ! [SY281: $i] :
~ ( in @ SY281 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(281,plain,
! [SV17: $i,SV54: $i] :
( ( ! [SY288: $i] :
( ~ ( in @ SV54 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SY288 @ ( sK12_B @ SV17 ) )
| ! [SY289: $i] :
( ~ ( in @ SY289 @ SV54 )
| ( in @ SY289 @ SY288 ) )
| ! [SY290: $i] :
( ~ ( in @ SY290 @ SY288 )
| ( in @ SY290 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(282,plain,
! [SV17: $i] :
( ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(283,plain,
! [SV38: $i,SV49: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV49 ) )
= $true )
| ( ( ~ ( in @ SV49 @ SV38 ) )
= $true )
| ( ( in @ SV44 @ ( setunion @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(284,plain,
! [SV39: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ ( sK5_B @ SV45 @ SV39 ) )
| ~ ( in @ ( sK5_B @ SV45 @ SV39 ) @ SV39 ) )
= $false )
| ( ( in @ SV45 @ ( setunion @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(285,plain,
! [SV9: $i,SV22: $i] :
( ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV22 )
= $false )
| ( ( in @ ( sK3_Xx @ SV22 @ SV9 ) @ SV9 )
= $false )
| ( ( SV9 = SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(286,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK21_SY86 @ SV30 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK20_Xx @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(287,plain,
! [SV40: $i,SV11: $i,SV46: $i] :
( ( ( SV46 = SV11 )
= $true )
| ( ( in @ SV46 @ SV40 )
= $true )
| ( ( in @ SV46 @ ( setadjoin @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(288,plain,
! [SV50: $i,SV11: $i,SV55: $i] :
( ( ( SV55 != SV11 )
| ( in @ SV55 @ ( setadjoin @ SV11 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(289,plain,
! [SV11: $i,SV51: $i,SV56: $i] :
( ( ~ ( in @ SV56 @ SV51 )
| ( in @ SV56 @ ( setadjoin @ SV11 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(290,plain,
! [SV23: $i,SV12: $i > $i > $o] :
( ( ( ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(291,plain,
! [SV12: $i > $i > $o,SV23: $i] :
( ( ( ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(292,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
| ~ ( ( SV47
!= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(293,plain,
! [SV13: $i] :
( ( ( in @ ( sK6_Xx @ SV13 ) @ omega )
= $true )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(294,plain,
! [SV13: $i] :
( ( ( in @ ( sK6_Xx @ SV13 ) @ SV13 )
= $true )
| ( ( ~ ( in @ emptyset @ SV13 ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(295,plain,
! [SV13: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ omega )
| ( in @ SV57 @ SV13 ) )
= $true )
| ( ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 )
= $false )
| ( ( in @ emptyset @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(296,plain,
! [SV31: $i,SV14: $i > $o] :
( ( ( SV14 @ SV31 )
= $false )
| ( ( SV31
= ( sK17_SY56 @ SV31 @ SV14 ) )
= $false )
| ( ( SV14
@ ( descr
@ ^ [SY239: $i] : ( SV14 @ SY239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(297,plain,
! [SV48: $i] :
( ( ( in @ SV48 @ sK2_SY176 )
= $false )
| ( ( in @ SV48 @ sK1_A )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(298,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) )
= $false )
| ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(299,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( SV15 @ SV32 )
= $false )
| ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( ~ ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(300,plain,
! [SV36: $i,SV41: $i] :
( ( ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV41 )
= $true )
| ( ( in @ SV41 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(301,plain,
! [SV36: $i,SV41: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV36 ) )
= $true )
| ( ( in @ SV41 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(302,plain,
! [SV37: $i,SV42: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV42 ) )
= $true )
| ( ( in @ SV52 @ SV37 )
= $true )
| ( ( in @ SV42 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(303,plain,
! [SV33: $i,SV16: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ ( sK11_B @ SV16 ) ) )
= $true )
| ( ( ~ ( in @ SV53 @ SV16 ) )
= $true )
| ( ( in @ SV33 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(304,plain,
! [SV17: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 ) )
= $false )
| ( ( ! [SY281: $i] :
~ ( in @ SY281 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(305,plain,
! [SV17: $i,SV43: $i] :
( ( ( ~ ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 ) )
= $false )
| ( ( ! [SY281: $i] :
~ ( in @ SY281 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(306,plain,
! [SV58: $i,SV17: $i,SV54: $i] :
( ( ~ ( in @ SV54 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SV58 @ ( sK12_B @ SV17 ) )
| ! [SY291: $i] :
( ~ ( in @ SY291 @ SV54 )
| ( in @ SY291 @ SV58 ) )
| ! [SY292: $i] :
( ~ ( in @ SY292 @ SV58 )
| ( in @ SY292 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(307,plain,
! [SV17: $i] :
( ( ~ ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(308,plain,
! [SV17: $i] :
( ( ~ ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(309,plain,
! [SV38: $i,SV49: $i,SV44: $i] :
( ( ( in @ SV44 @ SV49 )
= $false )
| ( ( ~ ( in @ SV49 @ SV38 ) )
= $true )
| ( ( in @ SV44 @ ( setunion @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(310,plain,
! [SV39: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ ( sK5_B @ SV45 @ SV39 ) ) )
= $false )
| ( ( in @ SV45 @ ( setunion @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(311,plain,
! [SV39: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK5_B @ SV45 @ SV39 ) @ SV39 ) )
= $false )
| ( ( in @ SV45 @ ( setunion @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(312,plain,
! [SV50: $i,SV11: $i,SV55: $i] :
( ( ( SV55 != SV11 )
= $true )
| ( ( in @ SV55 @ ( setadjoin @ SV11 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(313,plain,
! [SV11: $i,SV51: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV51 ) )
= $true )
| ( ( in @ SV56 @ ( setadjoin @ SV11 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(314,plain,
! [SV23: $i,SV59: $i,SV12: $i > $i > $o] :
( ( ( ! [SY293: $i] :
( ~ ( SV12 @ SY293 @ SV59 )
| ~ ( in @ SY293 @ SV23 ) )
| ( in @ SV59 @ ( sK7_B @ SV23 @ SV12 ) ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(315,plain,
! [SV12: $i > $i > $o,SV23: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV60 )
| ~ ( in @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(316,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) ) )
= $false )
| ( ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(317,plain,
! [SV12: $i > $i > $o,SV23: $i,SV47: $i] :
( ( ( ~ ( ( SV47
!= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(318,plain,
! [SV13: $i] :
( ( ( in @ emptyset @ SV13 )
= $false )
| ( ( in @ ( sK6_Xx @ SV13 ) @ omega )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(319,plain,
! [SV13: $i] :
( ( ( in @ emptyset @ SV13 )
= $false )
| ( ( in @ ( sK6_Xx @ SV13 ) @ SV13 )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( in @ SY237 @ omega )
| ( in @ SY237 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(320,plain,
! [SV13: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ omega ) )
= $true )
| ( ( in @ SV57 @ SV13 )
= $true )
| ( ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 )
= $false )
| ( ( in @ emptyset @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(321,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) ) )
= $false )
| ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(322,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) )
= $false )
| ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(323,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) )
| ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) )
= $false )
| ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(324,plain,
! [SV36: $i,SV41: $i] :
( ( ( in @ ( sK4_Xx @ SV41 @ SV36 ) @ SV36 )
= $false )
| ( ( in @ SV41 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(325,plain,
! [SV37: $i,SV42: $i,SV52: $i] :
( ( ( in @ SV52 @ SV42 )
= $false )
| ( ( in @ SV52 @ SV37 )
= $true )
| ( ( in @ SV42 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(326,plain,
! [SV33: $i,SV16: $i,SV53: $i] :
( ( ( in @ SV53 @ ( sK11_B @ SV16 ) )
= $false )
| ( ( ~ ( in @ SV53 @ SV16 ) )
= $true )
| ( ( in @ SV33 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(327,plain,
! [SV17: $i,SV43: $i] :
( ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( ! [SY281: $i] :
~ ( in @ SY281 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(328,plain,
! [SV17: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 ) )
= $true )
| ( ( ! [SY281: $i] :
~ ( in @ SY281 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(329,plain,
! [SV58: $i,SV17: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ ( sK12_B @ SV17 ) )
| ~ ( in @ SV58 @ ( sK12_B @ SV17 ) ) )
= $true )
| ( ( ! [SY291: $i] :
( ~ ( in @ SY291 @ SV54 )
| ( in @ SY291 @ SV58 ) )
| ! [SY292: $i] :
( ~ ( in @ SY292 @ SV58 )
| ( in @ SY292 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(330,plain,
! [SV17: $i] :
( ( ! [SY253: $i] :
( ~ ( in @ SY253 @ ( sK12_B @ SV17 ) )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SY253 )
| ( in @ SY254 @ SV17 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(331,plain,
! [SV17: $i] :
( ( ! [SY255: $i,SY256: $i] :
( ~ ( in @ SY255 @ SV17 )
| ~ ( in @ SY256 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ~ ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) )
| ~ ( ( in @ SY255 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) )
| ( in @ SY256 @ ( sK13_SY204 @ SY256 @ SY255 @ SV17 ) ) ) ) )
| ( SY255 = SY256 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(332,plain,
! [SV44: $i,SV38: $i,SV49: $i] :
( ( ( in @ SV49 @ SV38 )
= $false )
| ( ( in @ SV44 @ SV49 )
= $false )
| ( ( in @ SV44 @ ( setunion @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(333,plain,
! [SV39: $i,SV45: $i] :
( ( ( in @ SV45 @ ( sK5_B @ SV45 @ SV39 ) )
= $true )
| ( ( in @ SV45 @ ( setunion @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(334,plain,
! [SV39: $i,SV45: $i] :
( ( ( in @ ( sK5_B @ SV45 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ SV45 @ ( setunion @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(335,plain,
! [SV50: $i,SV11: $i,SV55: $i] :
( ( ( SV55 = SV11 )
= $false )
| ( ( in @ SV55 @ ( setadjoin @ SV11 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(336,plain,
! [SV11: $i,SV51: $i,SV56: $i] :
( ( ( in @ SV56 @ SV51 )
= $false )
| ( ( in @ SV56 @ ( setadjoin @ SV11 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(337,plain,
! [SV23: $i,SV59: $i,SV12: $i > $i > $o] :
( ( ( ! [SY293: $i] :
( ~ ( SV12 @ SY293 @ SV59 )
| ~ ( in @ SY293 @ SV23 ) ) )
= $true )
| ( ( in @ SV59 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(338,plain,
! [SV12: $i > $i > $o,SV23: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ ( sK7_B @ SV23 @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ( SV12 @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV60 )
| ~ ( in @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(339,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(340,plain,
! [SV12: $i > $i > $o,SV23: $i,SV47: $i] :
( ( ( SV47
!= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(341,plain,
! [SV13: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ omega )
| ( in @ SV61 @ SV13 ) )
= $true )
| ( ( in @ ( sK6_Xx @ SV13 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(342,plain,
! [SV13: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ omega )
| ( in @ SV62 @ SV13 ) )
= $true )
| ( ( in @ ( sK6_Xx @ SV13 ) @ SV13 )
= $true )
| ( ( in @ emptyset @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(343,plain,
! [SV13: $i,SV57: $i] :
( ( ( in @ SV57 @ omega )
= $false )
| ( ( in @ SV57 @ SV13 )
= $true )
| ( ( in @ ( setadjoin @ ( sK6_Xx @ SV13 ) @ ( sK6_Xx @ SV13 ) ) @ SV13 )
= $false )
| ( ( in @ emptyset @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(344,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) ) )
= $true )
| ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(345,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK18_Xx @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(346,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) ) )
= $false )
| ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(347,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK18_Xx @ SV15 ) ) )
= $false )
| ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(348,plain,
! [SV33: $i,SV16: $i,SV53: $i] :
( ( ( in @ SV53 @ SV16 )
= $false )
| ( ( in @ SV53 @ ( sK11_B @ SV16 ) )
= $false )
| ( ( in @ SV33 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(349,plain,
! [SV17: $i,SV43: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV43 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(350,plain,
! [SV17: $i,SV43: $i] :
( ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( ! [SY281: $i] :
~ ( in @ SY281 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(351,plain,
! [SV58: $i,SV17: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ ( sK12_B @ SV17 ) ) )
= $true )
| ( ( ~ ( in @ SV58 @ ( sK12_B @ SV17 ) ) )
= $true )
| ( ( ! [SY291: $i] :
( ~ ( in @ SY291 @ SV54 )
| ( in @ SY291 @ SV58 ) )
| ! [SY292: $i] :
( ~ ( in @ SY292 @ SV58 )
| ( in @ SY292 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(352,plain,
! [SV17: $i,SV64: $i] :
( ( ~ ( in @ SV64 @ ( sK12_B @ SV17 ) )
| ! [SY294: $i] :
( ~ ( in @ SY294 @ SV64 )
| ( in @ SY294 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(353,plain,
! [SV17: $i,SV65: $i] :
( ( ! [SY295: $i] :
( ~ ( in @ SV65 @ SV17 )
| ~ ( in @ SY295 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SY295 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SY295 @ SV65 @ SV17 ) )
| ~ ( in @ SY295 @ ( sK13_SY204 @ SY295 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SY295 @ SV65 @ SV17 ) )
| ( in @ SY295 @ ( sK13_SY204 @ SY295 @ SV65 @ SV17 ) ) ) ) )
| ( SV65 = SY295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(354,plain,
! [SV23: $i,SV59: $i,SV66: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ SV66 @ SV59 )
| ~ ( in @ SV66 @ SV23 ) )
= $true )
| ( ( in @ SV59 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(355,plain,
! [SV12: $i > $i > $o,SV23: $i,SV60: $i] :
( ( ( in @ SV60 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( SV12 @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV60 )
| ~ ( in @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(356,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(357,plain,
! [SV12: $i > $i > $o,SV23: $i,SV47: $i] :
( ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( ~ ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(358,plain,
! [SV13: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ omega ) )
= $true )
| ( ( in @ SV61 @ SV13 )
= $true )
| ( ( in @ ( sK6_Xx @ SV13 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(359,plain,
! [SV13: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ omega ) )
= $true )
| ( ( in @ SV62 @ SV13 )
= $true )
| ( ( in @ ( sK6_Xx @ SV13 ) @ SV13 )
= $true )
| ( ( in @ emptyset @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(360,plain,
! [SV32: $i,SV67: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV67 )
| ( ( sK18_Xx @ SV15 )
= SV67 ) )
= $true )
| ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(361,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( ! [SY241: $i] :
( ~ ( SV15 @ SY241 )
| ( ( sK18_Xx @ SV15 )
= SY241 ) ) )
= $true )
| ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(362,plain,
! [SV32: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK18_Xx @ SV15 ) )
= $true )
| ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(363,plain,
! [SV17: $i,SV43: $i,SV63: $i] :
( ( ( in @ SV63 @ SV43 )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(364,plain,
! [SV17: $i,SV43: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ SV43 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(365,plain,
! [SV58: $i,SV17: $i,SV54: $i] :
( ( ( in @ SV54 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( ~ ( in @ SV58 @ ( sK12_B @ SV17 ) ) )
= $true )
| ( ( ! [SY291: $i] :
( ~ ( in @ SY291 @ SV54 )
| ( in @ SY291 @ SV58 ) )
| ! [SY292: $i] :
( ~ ( in @ SY292 @ SV58 )
| ( in @ SY292 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(366,plain,
! [SV17: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ ( sK12_B @ SV17 ) ) )
= $true )
| ( ( ! [SY294: $i] :
( ~ ( in @ SY294 @ SV64 )
| ( in @ SY294 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(367,plain,
! [SV69: $i,SV17: $i,SV65: $i] :
( ( ~ ( in @ SV65 @ SV17 )
| ~ ( in @ SV69 @ SV17 )
| ~ ( ~ ( in @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) ) )
| ( SV65 = SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(368,plain,
! [SV23: $i,SV59: $i,SV66: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ SV66 @ SV59 ) )
= $true )
| ( ( ~ ( in @ SV66 @ SV23 ) )
= $true )
| ( ( in @ SV59 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(369,plain,
! [SV23: $i,SV60: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV60 )
| ~ ( in @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV23 ) )
= $false )
| ( ( in @ SV60 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(370,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(371,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( ~ ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(372,plain,
! [SV13: $i,SV61: $i] :
( ( ( in @ SV61 @ omega )
= $false )
| ( ( in @ SV61 @ SV13 )
= $true )
| ( ( in @ ( sK6_Xx @ SV13 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(373,plain,
! [SV13: $i,SV62: $i] :
( ( ( in @ SV62 @ omega )
= $false )
| ( ( in @ SV62 @ SV13 )
= $true )
| ( ( in @ ( sK6_Xx @ SV13 ) @ SV13 )
= $true )
| ( ( in @ emptyset @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(374,plain,
! [SV32: $i,SV67: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV67 ) )
= $true )
| ( ( ( sK18_Xx @ SV15 )
= SV67 )
= $true )
| ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(375,plain,
! [SV32: $i,SV70: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV70 )
| ( ( sK18_Xx @ SV15 )
= SV70 ) )
= $true )
| ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(376,plain,
! [SV63: $i,SV43: $i,SV17: $i] :
( ( ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(377,plain,
! [SV17: $i,SV43: $i,SV68: $i] :
( ( ( in @ SV68 @ SV43 )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(378,plain,
! [SV54: $i,SV17: $i,SV58: $i] :
( ( ( in @ SV58 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ SV54 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( ! [SY291: $i] :
( ~ ( in @ SY291 @ SV54 )
| ( in @ SY291 @ SV58 ) )
| ! [SY292: $i] :
( ~ ( in @ SY292 @ SV58 )
| ( in @ SY292 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(379,plain,
! [SV17: $i,SV64: $i] :
( ( ( in @ SV64 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( ! [SY294: $i] :
( ~ ( in @ SY294 @ SV64 )
| ( in @ SY294 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(380,plain,
! [SV69: $i,SV17: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ SV17 )
| ~ ( in @ SV69 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) ) )
| ( SV65 = SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(381,plain,
! [SV23: $i,SV59: $i,SV66: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ SV66 @ SV59 )
= $false )
| ( ( ~ ( in @ SV66 @ SV23 ) )
= $true )
| ( ( in @ SV59 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(382,plain,
! [SV23: $i,SV60: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV60 ) )
= $false )
| ( ( in @ SV60 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(383,plain,
! [SV12: $i > $i > $o,SV23: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV23 ) )
= $false )
| ( ( in @ SV60 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(384,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(385,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i] :
( ( ( ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(386,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) )
| ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $false )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(387,plain,
! [SV32: $i,SV67: $i,SV15: $i > $o] :
( ( ( SV15 @ SV67 )
= $false )
| ( ( ( sK18_Xx @ SV15 )
= SV67 )
= $true )
| ( ( SV15 @ ( sK19_SY73 @ SV32 @ SV15 ) )
= $true )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(388,plain,
! [SV32: $i,SV70: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV70 ) )
= $true )
| ( ( ( sK18_Xx @ SV15 )
= SV70 )
= $true )
| ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(389,plain,
! [SV63: $i,SV43: $i,SV17: $i] :
( ( ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(390,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(391,plain,
! [SV68: $i,SV43: $i,SV17: $i] :
( ( ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(392,plain,
! [SV17: $i,SV58: $i,SV54: $i] :
( ( ( ! [SY291: $i] :
( ~ ( in @ SY291 @ SV54 )
| ( in @ SY291 @ SV58 ) ) )
= $true )
| ( ( ! [SY292: $i] :
( ~ ( in @ SY292 @ SV58 )
| ( in @ SY292 @ SV54 ) ) )
= $true )
| ( ( in @ SV54 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ SV58 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(393,plain,
! [SV17: $i,SV64: $i,SV71: $i] :
( ( ( ~ ( in @ SV71 @ SV64 )
| ( in @ SV71 @ SV17 ) )
= $true )
| ( ( in @ SV64 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(394,plain,
! [SV69: $i,SV17: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ SV17 ) )
= $true )
| ( ( ~ ( in @ SV69 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) ) )
| ( SV65 = SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(395,plain,
! [SV59: $i,SV12: $i > $i > $o,SV23: $i,SV66: $i] :
( ( ( in @ SV66 @ SV23 )
= $false )
| ( ( SV12 @ SV66 @ SV59 )
= $false )
| ( ( in @ SV59 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(396,plain,
! [SV23: $i,SV60: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV60 )
= $true )
| ( ( in @ SV60 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(397,plain,
! [SV12: $i > $i > $o,SV23: $i,SV60: $i] :
( ( ( in @ ( sK8_Xy @ SV60 @ SV23 @ SV12 ) @ SV23 )
= $true )
| ( ( in @ SV60 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( in @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(398,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(399,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i] :
( ( ( ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(400,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ~ ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) ) )
= $false )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(401,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i] :
( ( ( ~ ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $false )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(402,plain,
! [SV32: $i,SV70: $i,SV15: $i > $o] :
( ( ( SV15 @ SV70 )
= $false )
| ( ( ( sK18_Xx @ SV15 )
= SV70 )
= $true )
| ( ( SV32
= ( sK19_SY73 @ SV32 @ SV15 ) )
= $false )
| ( ( SV15 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(403,plain,
! [SV63: $i,SV43: $i,SV17: $i] :
( ( ( ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(404,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(405,plain,
! [SV68: $i,SV43: $i,SV17: $i] :
( ( ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(406,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(407,plain,
! [SV17: $i,SV58: $i,SV54: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ SV54 )
| ( in @ SV72 @ SV58 ) )
= $true )
| ( ( ! [SY292: $i] :
( ~ ( in @ SY292 @ SV58 )
| ( in @ SY292 @ SV54 ) ) )
= $true )
| ( ( in @ SV54 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ SV58 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(408,plain,
! [SV17: $i,SV64: $i,SV71: $i] :
( ( ( ~ ( in @ SV71 @ SV64 ) )
= $true )
| ( ( in @ SV71 @ SV17 )
= $true )
| ( ( in @ SV64 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(409,plain,
! [SV69: $i,SV17: $i,SV65: $i] :
( ( ( in @ SV65 @ SV17 )
= $false )
| ( ( ~ ( in @ SV69 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) ) )
| ( SV65 = SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(410,plain,
! [SV47: $i,SV23: $i,SV73: $i,SV12: $i > $i > $o] :
( ( ( ! [SY296: $i] :
( ~ ( SV12 @ SY296 @ SV73 )
| ~ ( in @ SY296 @ SV23 ) )
| ( in @ SV73 @ ( sK7_B @ SV23 @ SV12 ) ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(411,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV74 )
| ~ ( in @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(412,plain,
! [SV47: $i,SV23: $i,SV12: $i > $i > $o] :
( ( ( ! [SY264: $i] :
( ! [SY265: $i] :
( ~ ( SV12 @ SY265 @ SY264 )
| ~ ( in @ SY265 @ SV23 ) )
| ( in @ SY264 @ ( sK7_B @ SV23 @ SV12 ) ) ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(413,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i] :
( ( ( ! [SY266: $i] :
( ~ ( in @ SY266 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SY266 )
| ~ ( in @ ( sK8_Xy @ SY266 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(414,plain,
! [SV63: $i,SV43: $i,SV17: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ ( sK12_B @ SV17 ) )
| ! [SY297: $i] :
( ~ ( in @ SY297 @ SV75 )
| ( in @ SY297 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV75 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(415,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(416,plain,
! [SV68: $i,SV43: $i,SV17: $i] :
( ( ( ! [SY282: $i] :
( ~ ( in @ SY282 @ ( sK12_B @ SV17 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SY282 )
| ( in @ SY283 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SY282 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(417,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(418,plain,
! [SV17: $i,SV58: $i,SV54: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ SV54 ) )
= $true )
| ( ( in @ SV72 @ SV58 )
= $true )
| ( ( ! [SY292: $i] :
( ~ ( in @ SY292 @ SV58 )
| ( in @ SY292 @ SV54 ) ) )
= $true )
| ( ( in @ SV54 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ SV58 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(419,plain,
! [SV17: $i,SV64: $i,SV71: $i] :
( ( ( in @ SV71 @ SV64 )
= $false )
| ( ( in @ SV71 @ SV17 )
= $true )
| ( ( in @ SV64 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(420,plain,
! [SV65: $i,SV17: $i,SV69: $i] :
( ( ( in @ SV69 @ SV17 )
= $false )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) ) )
| ( SV65 = SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(421,plain,
! [SV47: $i,SV23: $i,SV73: $i,SV12: $i > $i > $o] :
( ( ( ! [SY296: $i] :
( ~ ( SV12 @ SY296 @ SV73 )
| ~ ( in @ SY296 @ SV23 ) ) )
= $true )
| ( ( in @ SV73 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(422,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ ( sK7_B @ SV23 @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ( SV12 @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV74 )
| ~ ( in @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(423,plain,
! [SV47: $i,SV23: $i,SV76: $i,SV12: $i > $i > $o] :
( ( ( ! [SY298: $i] :
( ~ ( SV12 @ SY298 @ SV76 )
| ~ ( in @ SY298 @ SV23 ) )
| ( in @ SV76 @ ( sK7_B @ SV23 @ SV12 ) ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(424,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ ( sK7_B @ SV23 @ SV12 ) )
| ~ ( ~ ( SV12 @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV77 )
| ~ ( in @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(425,plain,
! [SV63: $i,SV43: $i,SV17: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ ( sK12_B @ SV17 ) ) )
= $true )
| ( ( ! [SY297: $i] :
( ~ ( in @ SY297 @ SV75 )
| ( in @ SY297 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV75 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(426,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(427,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(428,plain,
! [SV68: $i,SV43: $i,SV17: $i,SV78: $i] :
( ( ( ~ ( in @ SV78 @ ( sK12_B @ SV17 ) )
| ! [SY299: $i] :
( ~ ( in @ SY299 @ SV78 )
| ( in @ SY299 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV78 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(429,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
| ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(430,plain,
! [SV17: $i,SV58: $i,SV54: $i,SV72: $i] :
( ( ( in @ SV72 @ SV54 )
= $false )
| ( ( in @ SV72 @ SV58 )
= $true )
| ( ( ! [SY292: $i] :
( ~ ( in @ SY292 @ SV58 )
| ( in @ SY292 @ SV54 ) ) )
= $true )
| ( ( in @ SV54 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ SV58 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(431,plain,
! [SV17: $i,SV65: $i,SV69: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) ) ) )
= $true )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(432,plain,
! [SV47: $i,SV23: $i,SV73: $i,SV79: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ SV79 @ SV73 )
| ~ ( in @ SV79 @ SV23 ) )
= $true )
| ( ( in @ SV73 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(433,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV74: $i] :
( ( ( in @ SV74 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( SV12 @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV74 )
| ~ ( in @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(434,plain,
! [SV47: $i,SV23: $i,SV76: $i,SV12: $i > $i > $o] :
( ( ( ! [SY298: $i] :
( ~ ( SV12 @ SY298 @ SV76 )
| ~ ( in @ SY298 @ SV23 ) ) )
= $true )
| ( ( in @ SV76 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(435,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ ( sK7_B @ SV23 @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ( SV12 @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV77 )
| ~ ( in @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(436,plain,
! [SV63: $i,SV43: $i,SV17: $i,SV75: $i] :
( ( ( in @ SV75 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( ! [SY297: $i] :
( ~ ( in @ SY297 @ SV75 )
| ( in @ SY297 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV75 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(437,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(438,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(439,plain,
! [SV68: $i,SV43: $i,SV17: $i,SV78: $i] :
( ( ( ~ ( in @ SV78 @ ( sK12_B @ SV17 ) ) )
= $true )
| ( ( ! [SY299: $i] :
( ~ ( in @ SY299 @ SV78 )
| ( in @ SY299 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV78 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(440,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(441,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(442,plain,
! [SV17: $i,SV72: $i,SV54: $i,SV58: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV58 )
| ( in @ SV80 @ SV54 ) )
= $true )
| ( ( in @ SV72 @ SV58 )
= $true )
| ( ( in @ SV72 @ SV54 )
= $false )
| ( ( in @ SV54 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ SV58 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(443,plain,
! [SV17: $i,SV65: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) ) )
= $false )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(444,plain,
! [SV47: $i,SV23: $i,SV73: $i,SV79: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ SV79 @ SV73 ) )
= $true )
| ( ( ~ ( in @ SV79 @ SV23 ) )
= $true )
| ( ( in @ SV73 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(445,plain,
! [SV47: $i,SV23: $i,SV74: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV74 )
| ~ ( in @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV23 ) )
= $false )
| ( ( in @ SV74 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(446,plain,
! [SV47: $i,SV23: $i,SV76: $i,SV81: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ SV81 @ SV76 )
| ~ ( in @ SV81 @ SV23 ) )
= $true )
| ( ( in @ SV76 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(447,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV77: $i] :
( ( ( in @ SV77 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( SV12 @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV77 )
| ~ ( in @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(448,plain,
! [SV63: $i,SV17: $i,SV43: $i,SV75: $i] :
( ( ( ! [SY297: $i] :
( ~ ( in @ SY297 @ SV75 )
| ( in @ SY297 @ ( sK14_SY191 @ SV43 @ SV17 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV75 )
= $true )
| ( ( in @ SV75 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(449,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(450,plain,
! [SV63: $i,SV17: $i,SV43: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SV82 @ SV43 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(451,plain,
! [SV68: $i,SV43: $i,SV17: $i,SV78: $i] :
( ( ( in @ SV78 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( ! [SY299: $i] :
( ~ ( in @ SY299 @ SV78 )
| ( in @ SY299 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
| ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV78 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(452,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(453,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SY284 @ SV43 ) ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(454,plain,
! [SV17: $i,SV72: $i,SV54: $i,SV58: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV58 ) )
= $true )
| ( ( in @ SV80 @ SV54 )
= $true )
| ( ( in @ SV72 @ SV58 )
= $true )
| ( ( in @ SV72 @ SV54 )
= $false )
| ( ( in @ SV54 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ SV58 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(455,plain,
! [SV17: $i,SV65: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) ) )
= $false )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(456,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) ) )
= $false )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(457,plain,
! [SV47: $i,SV23: $i,SV73: $i,SV79: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ SV79 @ SV73 )
= $false )
| ( ( ~ ( in @ SV79 @ SV23 ) )
= $true )
| ( ( in @ SV73 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(458,plain,
! [SV47: $i,SV23: $i,SV74: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV74 ) )
= $false )
| ( ( in @ SV74 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(459,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV23 ) )
= $false )
| ( ( in @ SV74 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(460,plain,
! [SV47: $i,SV23: $i,SV76: $i,SV81: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ SV81 @ SV76 ) )
= $true )
| ( ( ~ ( in @ SV81 @ SV23 ) )
= $true )
| ( ( in @ SV76 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(461,plain,
! [SV47: $i,SV23: $i,SV77: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV77 )
| ~ ( in @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV23 ) )
= $false )
| ( ( in @ SV77 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(462,plain,
! [SV63: $i,SV17: $i,SV43: $i,SV75: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV75 )
| ( in @ SV83 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
= $true )
| ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV75 )
= $true )
| ( ( in @ SV75 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(463,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(464,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(465,plain,
! [SV63: $i,SV17: $i,SV43: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
= $true )
| ( ( ~ ( in @ SV82 @ SV43 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(466,plain,
! [SV68: $i,SV17: $i,SV43: $i,SV78: $i] :
( ( ( ! [SY299: $i] :
( ~ ( in @ SY299 @ SV78 )
| ( in @ SY299 @ ( sK14_SY191 @ SV43 @ SV17 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV78 )
= $true )
| ( ( in @ SV78 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(467,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
| ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(468,plain,
! [SV68: $i,SV17: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ ( sK14_SY191 @ SV43 @ SV17 ) )
| ~ ( in @ SV84 @ SV43 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(469,plain,
! [SV17: $i,SV72: $i,SV54: $i,SV58: $i,SV80: $i] :
( ( ( in @ SV80 @ SV58 )
= $false )
| ( ( in @ SV80 @ SV54 )
= $true )
| ( ( in @ SV72 @ SV58 )
= $true )
| ( ( in @ SV72 @ SV54 )
= $false )
| ( ( in @ SV54 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ SV58 @ ( sK12_B @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(470,plain,
! [SV17: $i,SV65: $i,SV69: $i] :
( ( ( in @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) @ ( sK12_B @ SV17 ) )
= $true )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(471,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) ) )
= $true )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(472,plain,
! [SV47: $i,SV73: $i,SV12: $i > $i > $o,SV23: $i,SV79: $i] :
( ( ( in @ SV79 @ SV23 )
= $false )
| ( ( SV12 @ SV79 @ SV73 )
= $false )
| ( ( in @ SV73 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(473,plain,
! [SV47: $i,SV23: $i,SV74: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV74 )
= $true )
| ( ( in @ SV74 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(474,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV74: $i] :
( ( ( in @ ( sK8_Xy @ SV74 @ SV23 @ SV12 ) @ SV23 )
= $true )
| ( ( in @ SV74 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(475,plain,
! [SV47: $i,SV23: $i,SV76: $i,SV81: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ SV81 @ SV76 )
= $false )
| ( ( ~ ( in @ SV81 @ SV23 ) )
= $true )
| ( ( in @ SV76 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(476,plain,
! [SV47: $i,SV23: $i,SV77: $i,SV12: $i > $i > $o] :
( ( ( ~ ( SV12 @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV77 ) )
= $false )
| ( ( in @ SV77 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(477,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV23 ) )
= $false )
| ( ( in @ SV77 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(478,plain,
! [SV63: $i,SV17: $i,SV43: $i,SV75: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV75 ) )
= $true )
| ( ( in @ SV83 @ ( sK14_SY191 @ SV43 @ SV17 ) )
= $true )
| ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV75 )
= $true )
| ( ( in @ SV75 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(479,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(480,plain,
! [SV63: $i,SV17: $i,SV43: $i] :
( ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(481,plain,
! [SV63: $i,SV17: $i,SV43: $i,SV82: $i] :
( ( ( in @ SV82 @ ( sK14_SY191 @ SV43 @ SV17 ) )
= $false )
| ( ( ~ ( in @ SV82 @ SV43 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(482,plain,
! [SV68: $i,SV17: $i,SV43: $i,SV78: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ SV78 )
| ( in @ SV85 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
= $true )
| ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV78 )
= $true )
| ( ( in @ SV78 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(483,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(484,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(485,plain,
! [SV68: $i,SV17: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ ( sK14_SY191 @ SV43 @ SV17 ) ) )
= $true )
| ( ( ~ ( in @ SV84 @ SV43 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(486,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
| ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) )
= $false )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(487,plain,
! [SV47: $i,SV76: $i,SV12: $i > $i > $o,SV23: $i,SV81: $i] :
( ( ( in @ SV81 @ SV23 )
= $false )
| ( ( SV12 @ SV81 @ SV76 )
= $false )
| ( ( in @ SV76 @ ( sK7_B @ SV23 @ SV12 ) )
= $true )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(488,plain,
! [SV47: $i,SV23: $i,SV77: $i,SV12: $i > $i > $o] :
( ( ( SV12 @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV77 )
= $true )
| ( ( in @ SV77 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(489,plain,
! [SV47: $i,SV12: $i > $i > $o,SV23: $i,SV77: $i] :
( ( ( in @ ( sK8_Xy @ SV77 @ SV23 @ SV12 ) @ SV23 )
= $true )
| ( ( in @ SV77 @ ( sK7_B @ SV23 @ SV12 ) )
= $false )
| ( ( SV47
= ( sK10_SY186 @ SV47 @ SV23 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK9_SY23 @ SV23 @ SV12 ) @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(490,plain,
! [SV63: $i,SV17: $i,SV43: $i,SV75: $i,SV83: $i] :
( ( ( in @ SV83 @ SV75 )
= $false )
| ( ( in @ SV83 @ ( sK14_SY191 @ SV43 @ SV17 ) )
= $true )
| ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV75 )
= $true )
| ( ( in @ SV75 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(491,plain,
! [SV63: $i,SV17: $i,SV43: $i,SV82: $i] :
( ( ( in @ SV82 @ SV43 )
= $false )
| ( ( in @ SV82 @ ( sK14_SY191 @ SV43 @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ SV63 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(492,plain,
! [SV68: $i,SV17: $i,SV43: $i,SV78: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ SV78 ) )
= $true )
| ( ( in @ SV85 @ ( sK14_SY191 @ SV43 @ SV17 ) )
= $true )
| ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV78 )
= $true )
| ( ( in @ SV78 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(493,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( in @ ( sK14_SY191 @ SV43 @ SV17 ) @ ( sK12_B @ SV17 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(494,plain,
! [SV68: $i,SV17: $i,SV43: $i] :
( ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV43 )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(495,plain,
! [SV68: $i,SV17: $i,SV43: $i,SV84: $i] :
( ( ( in @ SV84 @ ( sK14_SY191 @ SV43 @ SV17 ) )
= $false )
| ( ( ~ ( in @ SV84 @ SV43 ) )
= $true )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(496,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( ~ ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) )
= $false )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(497,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( ~ ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) ) )
= $false )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(498,plain,
! [SV68: $i,SV17: $i,SV43: $i,SV78: $i,SV85: $i] :
( ( ( in @ SV85 @ SV78 )
= $false )
| ( ( in @ SV85 @ ( sK14_SY191 @ SV43 @ SV17 ) )
= $true )
| ( ( in @ ( sK15_SY205 @ SV43 @ SV17 ) @ SV78 )
= $true )
| ( ( in @ SV78 @ ( sK12_B @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(499,plain,
! [SV68: $i,SV17: $i,SV43: $i,SV84: $i] :
( ( ( in @ SV84 @ SV43 )
= $false )
| ( ( in @ SV84 @ ( sK14_SY191 @ SV43 @ SV17 ) )
= $false )
| ( ( in @ ( sK16_Xx @ SV43 @ SV17 ) @ SV17 )
= $false )
| ( ( in @ SV68 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(500,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
= $true )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(501,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
| ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
= $true )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(502,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
= $true )
| ( ( ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
= $true )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(503,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
= $true )
| ( ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
= $true )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(504,plain,
! [SV17: $i,SV69: $i,SV65: $i] :
( ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
= $false )
| ( ( ~ ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) ) )
= $true )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(505,plain,
! [SV17: $i,SV65: $i,SV69: $i] :
( ( ( in @ SV69 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
= $false )
| ( ( in @ SV65 @ ( sK13_SY204 @ SV69 @ SV65 @ SV17 ) )
= $false )
| ( ( SV65 = SV69 )
= $true )
| ( ( in @ SV65 @ SV17 )
= $false )
| ( ( in @ SV69 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(506,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[61,505,503,499,498,494,493,491,490,489,488,487,480,479,474,473,472,470,469,419,402,397,396,395,387,373,372,362,348,345,343,336,335,334,333,332,325,324,300,297,296,287,286,285,271,260,252,247,234,232,218,181,180,159,158,157,156,155,154,136,113,104,103]) ).
thf(507,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU505^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n006.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 15:26:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.87/1.55
% 7.87/1.55 No.of.Axioms: 0
% 7.87/1.55
% 7.87/1.55 Length.of.Defs: 4997
% 7.87/1.55
% 7.87/1.55 Contains.Choice.Funs: true
% 7.87/1.55 .....................
% 7.87/1.55
% 7.87/1.55 ********************************
% 7.87/1.55 * All subproblems solved! *
% 7.87/1.55 ********************************
% 7.87/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,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:506,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.87/1.55
% 7.87/1.55 %**** Beginning of derivation protocol ****
% 7.87/1.55 % SZS output start CNFRefutation
% See solution above
% 7.87/1.56
% 7.87/1.56 %**** End of derivation protocol ****
% 7.87/1.56 %**** no. of clauses in derivation: 507 ****
% 7.87/1.56 %**** clause counter: 506 ****
% 7.87/1.56
% 7.87/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,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:506,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------