%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU520^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 10:44:44 AM UTC 2026
% Result : Theorem 1.59s 0.47s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 40
% Syntax : Number of formulae : 720 ( 283 unt; 0 typ; 39 def)
% Number of atoms : 5869 (1906 equ; 0 cnn)
% Maximal formula atoms : 37 ( 8 avg)
% Number of connectives : 13528 (2256 ~;2211 |; 128 &;8639 @)
% ( 21 <=>; 273 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 307 ( 307 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 73 usr; 41 con; 0-3 aty)
% Number of variables : 2572 ( 121 ^;2397 !; 54 ?;2572 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_emptyI,type,
emptyI: $o ).
thf(tp_emptyinPowerset,type,
emptyinPowerset: $o ).
thf(tp_emptyinunitempty,type,
emptyinunitempty: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_exuE3e,type,
exuE3e: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_noeltsimpempty,type,
noeltsimpempty: $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_nonemptyE1,type,
nonemptyE1: $o ).
thf(tp_nonemptyI,type,
nonemptyI: $o ).
thf(tp_nonemptyI1,type,
nonemptyI1: $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_powersetI,type,
powersetI: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK10_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_SY266,type,
sK12_SY266: $i > $i > $i > $i ).
thf(tp_sK13_SY253,type,
sK13_SY253: $i > $i > $i ).
thf(tp_sK14_SY267,type,
sK14_SY267: $i > $i > $i ).
thf(tp_sK15_Xx,type,
sK15_Xx: $i > $i > $i ).
thf(tp_sK16_SY53,type,
sK16_SY53: $i > ( $i > $o ) > $i ).
thf(tp_sK17_Xx,type,
sK17_Xx: ( $i > $o ) > $i ).
thf(tp_sK18_SY70,type,
sK18_SY70: $i > ( $i > $o ) > $i ).
thf(tp_sK19_Xx,type,
sK19_Xx: ( $i > $o ) > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY83,type,
sK20_SY83: $i > ( $i > $o ) > $i ).
thf(tp_sK21_Xx,type,
sK21_Xx: $i > $i > $i ).
thf(tp_sK22_Xx,type,
sK22_Xx: $i > $i > $i ).
thf(tp_sK23_Xx,type,
sK23_Xx: $i > $i ).
thf(tp_sK24_Xx,type,
sK24_Xx: $i > $i ).
thf(tp_sK25_Xx,type,
sK25_Xx: $i > $i ).
thf(tp_sK26_Xx,type,
sK26_Xx: $i > $i > $i ).
thf(tp_sK2_Xx,type,
sK2_Xx: $i > $i > $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: $i > $i > $i ).
thf(tp_sK4_B,type,
sK4_B: $i > $i > $i ).
thf(tp_sK5_Xx,type,
sK5_Xx: $i > $i ).
thf(tp_sK6_B,type,
sK6_B: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK7_Xy,type,
sK7_Xy: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK8_SY20,type,
sK8_SY20: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK9_SY248,type,
sK9_SY248: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setadjoinIR,type,
setadjoinIR: $o ).
thf(tp_setadjoinOr,type,
setadjoinOr: $o ).
thf(tp_setbeta,type,
setbeta: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setoftrueEq,type,
setoftrueEq: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(prop2set,definition,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(2,negated_conjecture,
( ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY18: $i > $i > $o,SY19: $i] :
( ! [SY20: $i] :
( ( in @ SY20 @ SY19 )
=> ? [SY22: $i] :
( ( SY18 @ SY20 @ SY22 )
& ! [SY23: $i] :
( ( SY18 @ SY20 @ SY23 )
=> ( SY22 = SY23 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY19 )
& ( SY18 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) )
=> ( ! [SY50: $i > $o] :
( ? [SY52: $i] :
( ( SY50 @ SY52 )
& ! [SY53: $i] :
( ( SY50 @ SY53 )
=> ( SY52 = SY53 ) ) )
=> ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY67: $i > $o] :
( ? [SY69: $i] :
( ( SY67 @ SY69 )
& ! [SY70: $i] :
( ( SY67 @ SY70 )
=> ( SY69 = SY70 ) ) )
=> ? [Xx: $i] :
( ( SY67 @ Xx )
& ! [Xy: $i] :
( ( SY67 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY73: $o,SY74: $i] :
( ( in @ SY74
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY75: $i] : SY73 ) )
=> SY73 )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY80: $i > $o] :
( ? [SY82: $i] :
( ( SY80 @ SY82 )
& ! [SY83: $i] :
( ( SY80 @ SY83 )
=> ( SY82 = SY83 ) ) )
=> ? [Xx: $i] : ( SY80 @ Xx ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) )
=> ( ! [SY97: $i] :
( ( SY97 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY97 ) )
=> ( ! [SY99: $i,SY100: $i > $o,SY101: $i] :
( ( in @ SY101 @ SY99 )
=> ( ( SY100 @ SY101 )
=> ( ( dsetconstr @ SY99
@ ^ [Xy: $i] : ( SY100 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY103: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY103 )
=> ( SY103 != emptyset ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [SY18: $i > $i > $o,SY19: $i] :
( ! [SY20: $i] :
( ( in @ SY20 @ SY19 )
=> ? [SY22: $i] :
( ( SY18 @ SY20 @ SY22 )
& ! [SY23: $i] :
( ( SY18 @ SY20 @ SY23 )
=> ( SY22 = SY23 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY19 )
& ( SY18 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY50: $i > $o] :
( ? [SY52: $i] :
( ( SY50 @ SY52 )
& ! [SY53: $i] :
( ( SY50 @ SY53 )
=> ( SY52 = SY53 ) ) )
=> ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY67: $i > $o] :
( ? [SY69: $i] :
( ( SY67 @ SY69 )
& ! [SY70: $i] :
( ( SY67 @ SY70 )
=> ( SY69 = SY70 ) ) )
=> ? [Xx: $i] :
( ( SY67 @ Xx )
& ! [Xy: $i] :
( ( SY67 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [SY73: $o,SY74: $i] :
( ( in @ SY74
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY75: $i] : SY73 ) )
=> SY73 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY80: $i > $o] :
( ? [SY82: $i] :
( ( SY80 @ SY82 )
& ! [SY83: $i] :
( ( SY80 @ SY83 )
=> ( SY82 = SY83 ) ) )
=> ? [Xx: $i] : ( SY80 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [SY97: $i] :
( ( SY97 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY97 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY99: $i,SY100: $i > $o,SY101: $i] :
( ( in @ SY101 @ SY99 )
=> ( ( SY100 @ SY101 )
=> ( ( dsetconstr @ SY99
@ ^ [Xy: $i] : ( SY100 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY103: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY103 )
=> ( SY103 != emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,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(37,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ~ ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[40]) ).
thf(42,plain,
( ( ~ ( in @ emptyset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK2_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK2_Xx @ B @ A ) @ A )
| ( in @ ( sK2_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(44,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(45,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK3_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(46,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK4_B @ Xx @ A ) )
& ( in @ ( sK4_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(47,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK5_Xx @ A ) @ omega )
& ( in @ ( sK5_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK5_Xx @ A ) @ ( sK5_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(49,plain,
( ( ! [SY18: $i > $i > $o,SY19: $i] :
( ( ( in @ ( sK8_SY20 @ SY19 @ SY18 ) @ SY19 )
& ! [SY247: $i] :
( ( ( SY18 @ ( sK8_SY20 @ SY19 @ SY18 ) @ ( sK9_SY248 @ SY247 @ SY19 @ SY18 ) )
& ( SY247
!= ( sK9_SY248 @ SY247 @ SY19 @ SY18 ) ) )
| ~ ( SY18 @ ( sK8_SY20 @ SY19 @ SY18 ) @ SY247 ) ) )
| ( ! [SY243: $i] :
( ! [Xy: $i] :
( ~ ( SY18 @ Xy @ SY243 )
| ~ ( in @ Xy @ SY19 ) )
| ( in @ SY243 @ ( sK6_B @ SY19 @ SY18 ) ) )
& ! [SY245: $i] :
( ~ ( in @ SY245 @ ( sK6_B @ SY19 @ SY18 ) )
| ( ( SY18 @ ( sK7_Xy @ SY245 @ SY19 @ SY18 ) @ SY245 )
& ( in @ ( sK7_Xy @ SY245 @ SY19 @ SY18 ) @ SY19 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(50,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK10_B @ A ) @ A )
& ! [SY249: $i] :
( ~ ( in @ SY249 @ ( sK10_B @ A ) )
| ~ ( in @ SY249 @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(51,plain,
( ( ! [A: $i] :
( ! [SY250: $i] :
( ( ( in @ ( sK15_Xx @ SY250 @ A ) @ SY250 )
& ~ ( in @ ( sK15_Xx @ SY250 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY250 )
| ( ! [SY271: $i] :
( ~ ( in @ SY271 @ ( sK11_B @ A ) )
| ! [SY269: $i] :
( ~ ( in @ SY269 @ SY271 )
| ( in @ SY269 @ ( sK13_SY253 @ SY250 @ A ) ) )
| ( in @ ( sK14_SY267 @ SY250 @ A ) @ SY271 ) )
& ( in @ ( sK13_SY253 @ SY250 @ A ) @ ( sK11_B @ A ) )
& ( in @ ( sK14_SY267 @ SY250 @ A ) @ SY250 )
& ! [SY270: $i] :
( ~ ( in @ SY270 @ ( sK13_SY253 @ SY250 @ A ) )
| ~ ( in @ SY270 @ SY250 ) ) ) )
& ! [SY258: $i,SY259: $i] :
( ~ ( in @ SY258 @ ( sK11_B @ A ) )
| ~ ( in @ SY259 @ ( sK11_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY258 )
| ( in @ Xx @ SY259 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY259 )
| ( in @ Xx @ SY258 ) ) )
& ! [SY262: $i] :
( ~ ( in @ SY262 @ ( sK11_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY262 )
| ( in @ Xx @ A ) ) )
& ! [SY264: $i,SY265: $i] :
( ~ ( in @ SY264 @ A )
| ~ ( in @ SY265 @ A )
| ( ( in @ ( sK12_SY266 @ SY265 @ SY264 @ A ) @ ( sK11_B @ A ) )
& ( ~ ( in @ SY264 @ ( sK12_SY266 @ SY265 @ SY264 @ A ) )
| ~ ( in @ SY265 @ ( sK12_SY266 @ SY265 @ SY264 @ A ) ) )
& ( ( in @ SY264 @ ( sK12_SY266 @ SY265 @ SY264 @ A ) )
| ( in @ SY265 @ ( sK12_SY266 @ SY265 @ SY264 @ A ) ) ) )
| ( SY264 = SY265 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(52,plain,
( ( ! [SY50: $i > $o] :
( ! [SY52: $i] :
( ( ( SY50 @ ( sK16_SY53 @ SY52 @ SY50 ) )
& ( SY52
!= ( sK16_SY53 @ SY52 @ SY50 ) ) )
| ~ ( SY50 @ SY52 ) )
| ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(53,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(54,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(55,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(56,plain,
( ( ! [SY67: $i > $o] :
( ! [SY69: $i] :
( ( ( SY67 @ ( sK18_SY70 @ SY69 @ SY67 ) )
& ( SY69
!= ( sK18_SY70 @ SY69 @ SY67 ) ) )
| ~ ( SY67 @ SY69 ) )
| ( ! [SY274: $i] :
( ~ ( SY67 @ SY274 )
| ( ( sK17_Xx @ SY67 )
= SY274 ) )
& ( SY67 @ ( sK17_Xx @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(57,plain,
( ( ! [SY73: $o] :
( ! [SY74: $i] :
~ ( in @ SY74
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY75: $i] : SY73 ) )
| SY73 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(58,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(59,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(60,plain,
( ( ! [SY80: $i > $o] :
( ! [SY82: $i] :
( ( ( SY80 @ ( sK20_SY83 @ SY82 @ SY80 ) )
& ( SY82
!= ( sK20_SY83 @ SY82 @ SY80 ) ) )
| ~ ( SY80 @ SY82 ) )
| ( SY80 @ ( sK19_Xx @ SY80 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK22_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK22_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK21_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK21_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(62,plain,
( ( ! [A: $i] :
( ( in @ ( sK23_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( in @ ( sK24_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(64,plain,
( ( ! [A: $i] :
( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
& ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(65,plain,
( ( ! [SY97: $i] :
( ( SY97 = emptyset )
| ( in @ ( sK25_Xx @ SY97 ) @ SY97 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(66,plain,
( ( ! [SY99: $i,SY100: $i > $o,SY101: $i] :
( ~ ( in @ SY101 @ SY99 )
| ~ ( SY100 @ SY101 )
| ( ( dsetconstr @ SY99
@ ^ [Xy: $i] : ( SY100 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(67,plain,
( ( ! [SY103: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ SY103 )
| ( SY103 != emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(68,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(69,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( ( ( Xy = Xx )
| ( in @ Xy @ A )
| ! [Xphi: $o] : Xphi )
& ( ( Xy = Xx )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xy @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(70,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK26_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK26_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(72,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK26_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK26_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(74,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(75,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(76,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( ( ( Xy = Xx )
| ( in @ Xy @ A )
| ! [Xphi: $o] : Xphi )
& ( ( Xy = Xx )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xy @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(77,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(78,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(79,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(80,plain,
( ( ! [SY103: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ SY103 )
| ( SY103 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(81,plain,
( ( ! [SY99: $i,SY100: $i > $o,SY101: $i] :
( ~ ( in @ SY101 @ SY99 )
| ~ ( SY100 @ SY101 )
| ( ( dsetconstr @ SY99
@ ^ [Xy: $i] : ( SY100 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(82,plain,
( ( ! [SY97: $i] :
( ( SY97 = emptyset )
| ( in @ ( sK25_Xx @ SY97 ) @ SY97 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(83,plain,
( ( ! [A: $i] :
( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
& ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(84,plain,
( ( ! [A: $i] :
( ( in @ ( sK24_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(85,plain,
( ( ! [A: $i] :
( ( in @ ( sK23_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK22_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK22_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK21_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK21_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(87,plain,
( ( ! [SY80: $i > $o] :
( ! [SY82: $i] :
( ( ( SY80 @ ( sK20_SY83 @ SY82 @ SY80 ) )
& ( SY82
!= ( sK20_SY83 @ SY82 @ SY80 ) ) )
| ~ ( SY80 @ SY82 ) )
| ( SY80 @ ( sK19_Xx @ SY80 ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(88,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(89,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(90,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(91,plain,
( ( ! [SY73: $o] :
( ! [SY74: $i] :
~ ( in @ SY74
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY75: $i] : SY73 ) )
| SY73 ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(92,plain,
( ( ! [SY67: $i > $o] :
( ! [SY69: $i] :
( ( ( SY67 @ ( sK18_SY70 @ SY69 @ SY67 ) )
& ( SY69
!= ( sK18_SY70 @ SY69 @ SY67 ) ) )
| ~ ( SY67 @ SY69 ) )
| ( ! [SY274: $i] :
( ~ ( SY67 @ SY274 )
| ( ( sK17_Xx @ SY67 )
= SY274 ) )
& ( SY67 @ ( sK17_Xx @ SY67 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(93,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(94,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(95,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)],[53]) ).
thf(96,plain,
( ( ! [SY50: $i > $o] :
( ! [SY52: $i] :
( ( ( SY50 @ ( sK16_SY53 @ SY52 @ SY50 ) )
& ( SY52
!= ( sK16_SY53 @ SY52 @ SY50 ) ) )
| ~ ( SY50 @ SY52 ) )
| ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(97,plain,
( ( ! [A: $i] :
( ! [SY250: $i] :
( ( ( in @ ( sK15_Xx @ SY250 @ A ) @ SY250 )
& ~ ( in @ ( sK15_Xx @ SY250 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY250 )
| ( ! [SY271: $i] :
( ~ ( in @ SY271 @ ( sK11_B @ A ) )
| ! [SY269: $i] :
( ~ ( in @ SY269 @ SY271 )
| ( in @ SY269 @ ( sK13_SY253 @ SY250 @ A ) ) )
| ( in @ ( sK14_SY267 @ SY250 @ A ) @ SY271 ) )
& ( in @ ( sK13_SY253 @ SY250 @ A ) @ ( sK11_B @ A ) )
& ( in @ ( sK14_SY267 @ SY250 @ A ) @ SY250 )
& ! [SY270: $i] :
( ~ ( in @ SY270 @ ( sK13_SY253 @ SY250 @ A ) )
| ~ ( in @ SY270 @ SY250 ) ) ) )
& ! [SY258: $i,SY259: $i] :
( ~ ( in @ SY258 @ ( sK11_B @ A ) )
| ~ ( in @ SY259 @ ( sK11_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY258 )
| ( in @ Xx @ SY259 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY259 )
| ( in @ Xx @ SY258 ) ) )
& ! [SY262: $i] :
( ~ ( in @ SY262 @ ( sK11_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY262 )
| ( in @ Xx @ A ) ) )
& ! [SY264: $i,SY265: $i] :
( ~ ( in @ SY264 @ A )
| ~ ( in @ SY265 @ A )
| ( ( in @ ( sK12_SY266 @ SY265 @ SY264 @ A ) @ ( sK11_B @ A ) )
& ( ~ ( in @ SY264 @ ( sK12_SY266 @ SY265 @ SY264 @ A ) )
| ~ ( in @ SY265 @ ( sK12_SY266 @ SY265 @ SY264 @ A ) ) )
& ( ( in @ SY264 @ ( sK12_SY266 @ SY265 @ SY264 @ A ) )
| ( in @ SY265 @ ( sK12_SY266 @ SY265 @ SY264 @ A ) ) ) )
| ( SY264 = SY265 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(98,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK10_B @ A ) @ A )
& ! [SY249: $i] :
( ~ ( in @ SY249 @ ( sK10_B @ A ) )
| ~ ( in @ SY249 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(99,plain,
( ( ! [SY18: $i > $i > $o,SY19: $i] :
( ( ( in @ ( sK8_SY20 @ SY19 @ SY18 ) @ SY19 )
& ! [SY247: $i] :
( ( ( SY18 @ ( sK8_SY20 @ SY19 @ SY18 ) @ ( sK9_SY248 @ SY247 @ SY19 @ SY18 ) )
& ( SY247
!= ( sK9_SY248 @ SY247 @ SY19 @ SY18 ) ) )
| ~ ( SY18 @ ( sK8_SY20 @ SY19 @ SY18 ) @ SY247 ) ) )
| ( ! [SY243: $i] :
( ! [Xy: $i] :
( ~ ( SY18 @ Xy @ SY243 )
| ~ ( in @ Xy @ SY19 ) )
| ( in @ SY243 @ ( sK6_B @ SY19 @ SY18 ) ) )
& ! [SY245: $i] :
( ~ ( in @ SY245 @ ( sK6_B @ SY19 @ SY18 ) )
| ( ( SY18 @ ( sK7_Xy @ SY245 @ SY19 @ SY18 ) @ SY245 )
& ( in @ ( sK7_Xy @ SY245 @ SY19 @ SY18 ) @ SY19 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(100,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK5_Xx @ A ) @ omega )
& ( in @ ( sK5_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK5_Xx @ A ) @ ( sK5_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(101,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(102,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(103,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK4_B @ Xx @ A ) )
& ( in @ ( sK4_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK3_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(105,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)],[44]) ).
thf(106,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK2_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK2_Xx @ B @ A ) @ A )
| ( in @ ( sK2_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(108,plain,
( ( ~ ( in @ emptyset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK22_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK22_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( in @ ( sK21_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK21_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(110,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
| ~ ! [SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(111,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK18_SY70 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK18_SY70 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK17_Xx @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK17_Xx @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(112,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_SY20 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK8_SY20 @ SX1 @ SX0 ) @ ( sK9_SY248 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK9_SY248 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ ( sK8_SY20 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( SX0 @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX2 @ ( sK6_B @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK6_B @ SX1 @ SX0 ) )
| ~ ( ~ ( SX0 @ ( sK7_Xy @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK7_Xy @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(113,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK15_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK11_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( sK13_SY253 @ SX1 @ SX0 ) ) )
| ( in @ ( sK14_SY267 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SX1 @ SX0 ) @ ( sK11_B @ SX0 ) )
| ~ ( in @ ( sK14_SY267 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK13_SY253 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK11_B @ SX0 ) )
| ~ ( in @ SX2 @ ( sK11_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK11_B @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SX2 @ SX1 @ SX0 ) @ ( sK11_B @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ SX1 @ ( sK12_SY266 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK12_SY266 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( in @ SX1 @ ( sK12_SY266 @ SX2 @ SX1 @ SX0 ) )
| ( in @ SX2 @ ( sK12_SY266 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK26_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK26_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(115,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK20_SY83 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK20_SY83 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ ( sK19_Xx @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(117,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)],[105,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(118,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ ( sK10_B @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK10_B @ SX0 ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(119,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SX0 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SX0 ) @ ( sK5_Xx @ SX0 ) ) @ SX0 ) )
| ~ ( in @ emptyset @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SX2 = SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(121,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK16_SY53 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK16_SY53 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(122,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK4_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_B @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(123,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyI,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,exu,exuE1,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,notinemptyset,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetI,prop2set,prop2setE,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,wellorderingAx]) ).
thf(124,plain,
! [SV1: $i] :
( ( in @ emptyset @ ( powerset @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(125,plain,
! [SV2: $i] :
( ( ( dsetconstr @ SV2
@ ^ [Xx: $i] : $true )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(126,plain,
! [SV3: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ~ ( in @ SY277 @ ( setadjoin @ SV3 @ SY276 ) )
| ( SY277 = SV3 )
| ( in @ SY277 @ SY276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(127,plain,
! [SV4: $i] :
( ( ! [SY278: $i,SY279: $i] :
( ~ ( in @ SY279 @ SY278 )
| ( in @ SY279 @ ( setadjoin @ SV4 @ SY278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(128,plain,
! [SV5: $i] :
( ( ! [SY280: $i] : ( in @ SV5 @ ( setadjoin @ SV5 @ SY280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(129,plain,
! [SV6: $i] :
( ( ! [SY281: $i] :
~ ( in @ SY281 @ SV6 )
| ( SV6 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(130,plain,
! [SV7: $i] :
( ( ! [SY282: $i > $o,SY283: $i] :
( ~ ( in @ SY283 @ SV7 )
| ~ ( SY282 @ SY283 )
| ( ( dsetconstr @ SV7
@ ^ [Xy: $i] : ( SY282 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(131,plain,
! [SV8: $i] :
( ( ( SV8 = emptyset )
| ( in @ ( sK25_Xx @ SV8 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(132,plain,
! [SV9: $i] :
( ( ( in @ ( sK24_Xx @ SV9 ) @ SV9 )
| ( SV9 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(133,plain,
! [SV10: $i] :
( ( ( in @ ( sK23_Xx @ SV10 ) @ SV10 )
| ( SV10 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(134,plain,
! [SV11: $i] :
( ( ~ ( in @ SV11 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(135,plain,
! [SV12: $i] :
( ( ~ ( in @ SV12 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(136,plain,
( ( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(137,plain,
! [SV13: $o] :
( ( ! [SY285: $i] :
~ ( in @ SY285
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY286: $i] : SV13 ) )
| SV13 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[91]) ).
thf(138,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[91]) ).
thf(139,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[91]) ).
thf(140,plain,
! [SV14: $i] :
( ( ! [SY287: $i > $o,SY288: $i] :
( ~ ( in @ SY288
@ ( dsetconstr @ SV14
@ ^ [Xy: $i] : ( SY287 @ Xy ) ) )
| ( SY287 @ SY288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(141,plain,
! [SV15: $i] :
( ( ! [SY290: $i > $o,SY291: $i] :
( ~ ( in @ SY291
@ ( dsetconstr @ SV15
@ ^ [Xy: $i] : ( SY290 @ Xy ) ) )
| ( in @ SY291 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(142,plain,
! [SV16: $i] :
( ( ! [SY293: $i > $o,SY294: $i] :
( ~ ( in @ SY294 @ SV16 )
| ~ ( SY293 @ SY294 )
| ( in @ SY294
@ ( dsetconstr @ SV16
@ ^ [Xy: $i] : ( SY293 @ Xy ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(143,plain,
! [SV17: $i] :
( ( ~ ( in @ SV17 @ omega )
| ( in @ ( setadjoin @ SV17 @ SV17 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(144,plain,
! [SV18: $i] :
( ( ~ ( in @ SV18 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(145,plain,
( ( in @ emptyset @ ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(146,plain,
! [SV19: $i] :
( ( ! [SY296: $i] :
( ~ ( ~ ( in @ ( sK22_Xx @ SY296 @ SV19 ) @ SV19 )
| ~ ~ ( in @ ( sK22_Xx @ SY296 @ SV19 ) @ SY296 ) )
| ~ ( ~ ( in @ ( sK21_Xx @ SY296 @ SV19 ) @ SY296 )
| ~ ~ ( in @ ( sK21_Xx @ SY296 @ SV19 ) @ SV19 ) )
| ( SV19 = SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(147,plain,
! [SV20: $i] :
( ( ~ ( ~ ! [SY297: $i > $o,SY298: $i] :
( ~ ( in @ SY298 @ SV20 )
| ~ ( SY297 @ SY298 )
| ( in @ SY298
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY297 @ SX3 ) ) ) )
| ~ ! [SY300: $i > $o,SY301: $i] :
( ~ ( in @ SY301 @ SV20 )
| ~ ( in @ SY301
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY300 @ SX3 ) ) )
| ( SY300 @ SY301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(148,plain,
! [SV21: $i > $o] :
( ( ! [SY303: $i] :
( ~ ( ~ ( SV21 @ ( sK18_SY70 @ SY303 @ SV21 ) )
| ~ ( ( SY303
!= ( sK18_SY70 @ SY303 @ SV21 ) ) ) )
| ~ ( SV21 @ SY303 ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(149,plain,
! [SV22: $i > $i > $o] :
( ( ! [SY305: $i] :
( ~ ( ~ ( in @ ( sK8_SY20 @ SY305 @ SV22 ) @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( ~ ( SV22 @ ( sK8_SY20 @ SY305 @ SV22 ) @ ( sK9_SY248 @ SY306 @ SY305 @ SV22 ) )
| ~ ( ( SY306
!= ( sK9_SY248 @ SY306 @ SY305 @ SV22 ) ) ) )
| ~ ( SV22 @ ( sK8_SY20 @ SY305 @ SV22 ) @ SY306 ) ) )
| ~ ( ~ ! [SY307: $i] :
( ! [SY308: $i] :
( ~ ( SV22 @ SY308 @ SY307 )
| ~ ( in @ SY308 @ SY305 ) )
| ( in @ SY307 @ ( sK6_B @ SY305 @ SV22 ) ) )
| ~ ! [SY309: $i] :
( ~ ( in @ SY309 @ ( sK6_B @ SY305 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY309 @ SY305 @ SV22 ) @ SY309 )
| ~ ( in @ ( sK7_Xy @ SY309 @ SY305 @ SV22 ) @ SY305 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(150,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY310: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SY310 @ SV23 ) @ SY310 )
| ~ ~ ( in @ ( sK15_Xx @ SY310 @ SV23 ) @ SV23 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY310 )
| ~ ( ~ ! [SY312: $i] :
( ~ ( in @ SY312 @ ( sK11_B @ SV23 ) )
| ! [SY313: $i] :
( ~ ( in @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK13_SY253 @ SY310 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SY310 @ SV23 ) @ SY312 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SY310 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SY310 @ SV23 ) @ SY310 ) )
| ~ ! [SY314: $i] :
( ~ ( in @ SY314 @ ( sK13_SY253 @ SY310 @ SV23 ) )
| ~ ( in @ SY314 @ SY310 ) ) ) ) )
| ~ ~ ( ~ ! [SY315: $i,SY316: $i] :
( ~ ( in @ SY315 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SY316 @ ( sK11_B @ SV23 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY315 )
| ( in @ SX3 @ SY316 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY316 )
| ( in @ SX3 @ SY315 ) ) )
| ~ ~ ( ~ ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(151,plain,
! [SV24: $i] :
( ( ! [SY323: $i] :
( ~ ( ~ ( in @ ( sK26_Xx @ SY323 @ SV24 ) @ SY323 )
| ~ ~ ( in @ ( sK26_Xx @ SY323 @ SV24 ) @ SV24 ) )
| ( in @ SY323 @ ( powerset @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(152,plain,
! [SV25: $i > $o] :
( ( ! [SY324: $i] :
( ~ ( ~ ( SV25 @ ( sK20_SY83 @ SY324 @ SV25 ) )
| ~ ( ( SY324
!= ( sK20_SY83 @ SY324 @ SV25 ) ) ) )
| ~ ( SV25 @ SY324 ) )
| ( SV25 @ ( sK19_Xx @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(153,plain,
! [SV26: $i] :
( ( ! [SY325: $i] :
( ~ ( ~ ( ~ ( in @ ( sK2_Xx @ SY325 @ SV26 ) @ SV26 )
| ~ ( in @ ( sK2_Xx @ SY325 @ SV26 ) @ SY325 ) )
| ~ ( ( in @ ( sK2_Xx @ SY325 @ SV26 ) @ SV26 )
| ( in @ ( sK2_Xx @ SY325 @ SV26 ) @ SY325 ) ) )
| ( SV26 = SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(154,plain,
! [SV27: $i] :
( ( ~ ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( in @ SY327 @ ( setadjoin @ SV27 @ SY326 ) )
| ( SY327 = SV27 )
| ( in @ SY327 @ SY326 ) )
| ~ ~ ( ~ ! [SY328: $i,SY329: $i] :
( ( SY329 != SV27 )
| ( in @ SY329 @ ( setadjoin @ SV27 @ SY328 ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ SY331 @ SY330 )
| ( in @ SY331 @ ( setadjoin @ SV27 @ SY330 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(155,plain,
! [SV28: $i] :
( ( ! [SY332: $i] :
~ ( in @ SY332 @ SV28 )
| ~ ( ~ ( in @ ( sK10_B @ SV28 ) @ SV28 )
| ~ ! [SY333: $i] :
( ~ ( in @ SY333 @ ( sK10_B @ SV28 ) )
| ~ ( in @ SY333 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(156,plain,
! [SV29: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV29 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV29 ) @ SV29 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 ) )
| ~ ( in @ emptyset @ SV29 )
| ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(157,plain,
! [SV30: $i] :
( ( ! [SY335: $i,SY336: $i] :
( ~ ( in @ SY336 @ ( setadjoin @ SV30 @ SY335 ) )
| ~ ( ~ ~ ( ~ ( ( SY336 = SV30 )
| ( in @ SY336 @ SY335 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY336 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY336 @ SY335 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(158,plain,
! [SV31: $i > $o] :
( ( ! [SY341: $i] :
( ~ ( ~ ( SV31 @ ( sK16_SY53 @ SY341 @ SV31 ) )
| ~ ( ( SY341
!= ( sK16_SY53 @ SY341 @ SV31 ) ) ) )
| ~ ( SV31 @ SY341 ) )
| ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(159,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK4_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(160,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(161,plain,
! [SV32: $i,SV3: $i] :
( ( ! [SY343: $i] :
( ~ ( in @ SY343 @ ( setadjoin @ SV3 @ SV32 ) )
| ( SY343 = SV3 )
| ( in @ SY343 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(162,plain,
! [SV4: $i,SV33: $i] :
( ( ! [SY344: $i] :
( ~ ( in @ SY344 @ SV33 )
| ( in @ SY344 @ ( setadjoin @ SV4 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(163,plain,
! [SV34: $i,SV5: $i] :
( ( in @ SV5 @ ( setadjoin @ SV5 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(164,plain,
! [SV6: $i] :
( ( ( ! [SY281: $i] :
~ ( in @ SY281 @ SV6 ) )
= $true )
| ( ( SV6 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(165,plain,
! [SV35: $i > $o,SV7: $i] :
( ( ! [SY345: $i] :
( ~ ( in @ SY345 @ SV7 )
| ~ ( SV35 @ SY345 )
| ( ( dsetconstr @ SV7
@ ^ [SY346: $i] : ( SV35 @ SY346 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(166,plain,
! [SV8: $i] :
( ( ( SV8 = emptyset )
= $true )
| ( ( in @ ( sK25_Xx @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(167,plain,
! [SV9: $i] :
( ( ( in @ ( sK24_Xx @ SV9 ) @ SV9 )
= $true )
| ( ( SV9 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(168,plain,
! [SV10: $i] :
( ( ( in @ ( sK23_Xx @ SV10 ) @ SV10 )
= $true )
| ( ( SV10 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(169,plain,
! [SV11: $i] :
( ( in @ SV11 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(170,plain,
! [SV12: $i] :
( ( in @ SV12 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(171,plain,
! [SV36: $i] :
( ( ( ~ ( in @ SV36 @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(172,plain,
! [SV13: $o] :
( ( ( ! [SY285: $i] :
~ ( in @ SY285
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY286: $i] : SV13 ) ) )
= $true )
| ( SV13 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(173,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(174,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(175,plain,
! [SV37: $i > $o,SV14: $i] :
( ( ! [SY347: $i] :
( ~ ( in @ SY347
@ ( dsetconstr @ SV14
@ ^ [SY348: $i] : ( SV37 @ SY348 ) ) )
| ( SV37 @ SY347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(176,plain,
! [SV38: $i > $o,SV15: $i] :
( ( ! [SY349: $i] :
( ~ ( in @ SY349
@ ( dsetconstr @ SV15
@ ^ [SY350: $i] : ( SV38 @ SY350 ) ) )
| ( in @ SY349 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(177,plain,
! [SV39: $i > $o,SV16: $i] :
( ( ! [SY351: $i] :
( ~ ( in @ SY351 @ SV16 )
| ~ ( SV39 @ SY351 )
| ( in @ SY351
@ ( dsetconstr @ SV16
@ ^ [SY352: $i] : ( SV39 @ SY352 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(178,plain,
! [SV17: $i] :
( ( ( ~ ( in @ SV17 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV17 @ SV17 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(179,plain,
! [SV18: $i] :
( ( in @ SV18 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(180,plain,
! [SV19: $i,SV40: $i] :
( ( ~ ( ~ ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
| ~ ~ ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 ) )
| ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
| ( SV19 = SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(181,plain,
! [SV20: $i] :
( ( ~ ! [SY297: $i > $o,SY298: $i] :
( ~ ( in @ SY298 @ SV20 )
| ~ ( SY297 @ SY298 )
| ( in @ SY298
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY297 @ SX3 ) ) ) )
| ~ ! [SY300: $i > $o,SY301: $i] :
( ~ ( in @ SY301 @ SV20 )
| ~ ( in @ SY301
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY300 @ SX3 ) ) )
| ( SY300 @ SY301 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(182,plain,
! [SV21: $i > $o] :
( ( ( ! [SY303: $i] :
( ~ ( ~ ( SV21 @ ( sK18_SY70 @ SY303 @ SV21 ) )
| ~ ( ( SY303
!= ( sK18_SY70 @ SY303 @ SV21 ) ) ) )
| ~ ( SV21 @ SY303 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(183,plain,
! [SV22: $i > $i > $o,SV41: $i] :
( ( ~ ( ~ ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
| ~ ! [SY353: $i] :
( ~ ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) )
| ~ ( ( SY353
!= ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) ) ) )
| ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SY353 ) ) )
| ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(184,plain,
! [SV23: $i] :
( ( ~ ! [SY310: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SY310 @ SV23 ) @ SY310 )
| ~ ~ ( in @ ( sK15_Xx @ SY310 @ SV23 ) @ SV23 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY310 )
| ~ ( ~ ! [SY312: $i] :
( ~ ( in @ SY312 @ ( sK11_B @ SV23 ) )
| ! [SY313: $i] :
( ~ ( in @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK13_SY253 @ SY310 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SY310 @ SV23 ) @ SY312 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SY310 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SY310 @ SV23 ) @ SY310 ) )
| ~ ! [SY314: $i] :
( ~ ( in @ SY314 @ ( sK13_SY253 @ SY310 @ SV23 ) )
| ~ ( in @ SY314 @ SY310 ) ) ) ) )
| ~ ~ ( ~ ! [SY315: $i,SY316: $i] :
( ~ ( in @ SY315 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SY316 @ ( sK11_B @ SV23 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY315 )
| ( in @ SX3 @ SY316 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY316 )
| ( in @ SX3 @ SY315 ) ) )
| ~ ~ ( ~ ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(185,plain,
! [SV24: $i,SV42: $i] :
( ( ~ ( ~ ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV42 )
| ~ ~ ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV24 ) )
| ( in @ SV42 @ ( powerset @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(186,plain,
! [SV25: $i > $o] :
( ( ( ! [SY324: $i] :
( ~ ( ~ ( SV25 @ ( sK20_SY83 @ SY324 @ SV25 ) )
| ~ ( ( SY324
!= ( sK20_SY83 @ SY324 @ SV25 ) ) ) )
| ~ ( SV25 @ SY324 ) ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(187,plain,
! [SV26: $i,SV43: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) )
| ~ ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) ) )
| ( SV26 = SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(188,plain,
! [SV27: $i] :
( ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( in @ SY327 @ ( setadjoin @ SV27 @ SY326 ) )
| ( SY327 = SV27 )
| ( in @ SY327 @ SY326 ) )
| ~ ~ ( ~ ! [SY328: $i,SY329: $i] :
( ( SY329 != SV27 )
| ( in @ SY329 @ ( setadjoin @ SV27 @ SY328 ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ SY331 @ SY330 )
| ( in @ SY331 @ ( setadjoin @ SV27 @ SY330 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(189,plain,
! [SV28: $i] :
( ( ( ! [SY332: $i] :
~ ( in @ SY332 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK10_B @ SV28 ) @ SV28 )
| ~ ! [SY333: $i] :
( ~ ( in @ SY333 @ ( sK10_B @ SV28 ) )
| ~ ( in @ SY333 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(190,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV29 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV29 ) @ SV29 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 ) )
| ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(191,plain,
! [SV44: $i,SV30: $i] :
( ( ! [SY357: $i] :
( ~ ( in @ SY357 @ ( setadjoin @ SV30 @ SV44 ) )
| ~ ( ~ ~ ( ~ ( ( SY357 = SV30 )
| ( in @ SY357 @ SV44 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY357 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY360: $o] :
( ~ SY360
| ( in @ SY357 @ SV44 )
| SY360 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(192,plain,
! [SV31: $i > $o] :
( ( ( ! [SY341: $i] :
( ~ ( ~ ( SV31 @ ( sK16_SY53 @ SY341 @ SV31 ) )
| ~ ( ( SY341
!= ( sK16_SY53 @ SY341 @ SV31 ) ) ) )
| ~ ( SV31 @ SY341 ) ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(193,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(194,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK4_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(195,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(196,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(197,plain,
! [SV32: $i,SV3: $i,SV45: $i] :
( ( ~ ( in @ SV45 @ ( setadjoin @ SV3 @ SV32 ) )
| ( SV45 = SV3 )
| ( in @ SV45 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(198,plain,
! [SV4: $i,SV33: $i,SV46: $i] :
( ( ~ ( in @ SV46 @ SV33 )
| ( in @ SV46 @ ( setadjoin @ SV4 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(199,plain,
! [SV6: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV6 ) )
= $true )
| ( ( SV6 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(200,plain,
! [SV35: $i > $o,SV7: $i,SV48: $i] :
( ( ~ ( in @ SV48 @ SV7 )
| ~ ( SV35 @ SV48 )
| ( ( dsetconstr @ SV7
@ ^ [SY346: $i] : ( SV35 @ SY346 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(201,plain,
! [SV36: $i] :
( ( ( in @ SV36 @ emptyset )
= $false )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(202,plain,
! [SV13: $o,SV49: $i] :
( ( ( ~ ( in @ SV49
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY286: $i] : SV13 ) ) )
= $true )
| ( SV13 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(203,plain,
! [SV50: $i] :
( ( ( ~ ( in @ SV50
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(204,plain,
! [SV51: $i] :
( ( ( ~ ( in @ SV51
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(205,plain,
! [SV37: $i > $o,SV14: $i,SV52: $i] :
( ( ~ ( in @ SV52
@ ( dsetconstr @ SV14
@ ^ [SY348: $i] : ( SV37 @ SY348 ) ) )
| ( SV37 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(206,plain,
! [SV38: $i > $o,SV15: $i,SV53: $i] :
( ( ~ ( in @ SV53
@ ( dsetconstr @ SV15
@ ^ [SY350: $i] : ( SV38 @ SY350 ) ) )
| ( in @ SV53 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(207,plain,
! [SV39: $i > $o,SV16: $i,SV54: $i] :
( ( ~ ( in @ SV54 @ SV16 )
| ~ ( SV39 @ SV54 )
| ( in @ SV54
@ ( dsetconstr @ SV16
@ ^ [SY352: $i] : ( SV39 @ SY352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(208,plain,
! [SV17: $i] :
( ( ( in @ SV17 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV17 @ SV17 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(209,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
| ~ ~ ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
| ( SV19 = SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(210,plain,
! [SV20: $i] :
( ( ~ ! [SY297: $i > $o,SY298: $i] :
( ~ ( in @ SY298 @ SV20 )
| ~ ( SY297 @ SY298 )
| ( in @ SY298
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY297 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(211,plain,
! [SV20: $i] :
( ( ~ ! [SY300: $i > $o,SY301: $i] :
( ~ ( in @ SY301 @ SV20 )
| ~ ( in @ SY301
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY300 @ SX3 ) ) )
| ( SY300 @ SY301 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(212,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ( ~ ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
| ~ ( ( SV55
!= ( sK18_SY70 @ SV55 @ SV21 ) ) ) )
| ~ ( SV21 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(213,plain,
! [SV22: $i > $i > $o,SV41: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
| ~ ! [SY353: $i] :
( ~ ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) )
| ~ ( ( SY353
!= ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) ) ) )
| ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SY353 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(214,plain,
! [SV23: $i] :
( ( ~ ! [SY310: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SY310 @ SV23 ) @ SY310 )
| ~ ~ ( in @ ( sK15_Xx @ SY310 @ SV23 ) @ SV23 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY310 )
| ~ ( ~ ! [SY312: $i] :
( ~ ( in @ SY312 @ ( sK11_B @ SV23 ) )
| ! [SY313: $i] :
( ~ ( in @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK13_SY253 @ SY310 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SY310 @ SV23 ) @ SY312 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SY310 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SY310 @ SV23 ) @ SY310 ) )
| ~ ! [SY314: $i] :
( ~ ( in @ SY314 @ ( sK13_SY253 @ SY310 @ SV23 ) )
| ~ ( in @ SY314 @ SY310 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(215,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY315: $i,SY316: $i] :
( ~ ( in @ SY315 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SY316 @ ( sK11_B @ SV23 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY315 )
| ( in @ SX3 @ SY316 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY316 )
| ( in @ SX3 @ SY315 ) ) )
| ~ ~ ( ~ ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(216,plain,
! [SV24: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV42 )
| ~ ~ ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( in @ SV42 @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(217,plain,
! [SV56: $i,SV25: $i > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK20_SY83 @ SV56 @ SV25 ) )
| ~ ( ( SV56
!= ( sK20_SY83 @ SV56 @ SV25 ) ) ) )
| ~ ( SV25 @ SV56 ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(218,plain,
! [SV26: $i,SV43: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) )
| ~ ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) ) ) )
= $true )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(219,plain,
! [SV27: $i] :
( ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( in @ SY327 @ ( setadjoin @ SV27 @ SY326 ) )
| ( SY327 = SV27 )
| ( in @ SY327 @ SY326 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(220,plain,
! [SV27: $i] :
( ( ~ ~ ( ~ ! [SY328: $i,SY329: $i] :
( ( SY329 != SV27 )
| ( in @ SY329 @ ( setadjoin @ SV27 @ SY328 ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ SY331 @ SY330 )
| ( in @ SY331 @ ( setadjoin @ SV27 @ SY330 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(221,plain,
! [SV28: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK10_B @ SV28 ) @ SV28 )
| ~ ! [SY333: $i] :
( ~ ( in @ SY333 @ ( sK10_B @ SV28 ) )
| ~ ( in @ SY333 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(222,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV29 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV29 ) @ SV29 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(223,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ~ ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
| ~ ( ~ ~ ( ~ ( ( SV58 = SV30 )
| ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV58 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY371: $o] :
( ~ SY371
| ( in @ SV58 @ SV44 )
| SY371 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(224,plain,
! [SV59: $i,SV31: $i > $o] :
( ( ( ~ ( ~ ( SV31 @ ( sK16_SY53 @ SV59 @ SV31 ) )
| ~ ( ( SV59
!= ( sK16_SY53 @ SV59 @ SV31 ) ) ) )
| ~ ( SV31 @ SV59 ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(225,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(226,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK4_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(227,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(228,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(229,plain,
! [SV32: $i,SV3: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ ( setadjoin @ SV3 @ SV32 ) ) )
= $true )
| ( ( ( SV45 = SV3 )
| ( in @ SV45 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(230,plain,
! [SV4: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV33 ) )
= $true )
| ( ( in @ SV46 @ ( setadjoin @ SV4 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(231,plain,
! [SV6: $i,SV47: $i] :
( ( ( in @ SV47 @ SV6 )
= $false )
| ( ( SV6 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(232,plain,
! [SV35: $i > $o,SV7: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV7 ) )
= $true )
| ( ( ~ ( SV35 @ SV48 )
| ( ( dsetconstr @ SV7
@ ^ [SY346: $i] : ( SV35 @ SY346 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(233,plain,
! [SV36: $i,SV60: $o] :
( ( SV60 = $true )
| ( ( in @ SV36 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[201]) ).
thf(234,plain,
! [SV36: $i] :
( ( $true = $true )
| ( ( in @ SV36 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[201]) ).
thf(235,plain,
! [SV36: $i] :
( ( $false = $true )
| ( ( in @ SV36 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[201]) ).
thf(236,plain,
! [SV13: $o,SV49: $i] :
( ( ( in @ SV49
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY286: $i] : SV13 ) )
= $false )
| ( SV13 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(237,plain,
! [SV50: $i] :
( ( ( in @ SV50
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(238,plain,
! [SV51: $i] :
( ( ( in @ SV51
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX1: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(239,plain,
! [SV37: $i > $o,SV14: $i,SV52: $i] :
( ( ( ~ ( in @ SV52
@ ( dsetconstr @ SV14
@ ^ [SY348: $i] : ( SV37 @ SY348 ) ) ) )
= $true )
| ( ( SV37 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(240,plain,
! [SV38: $i > $o,SV15: $i,SV53: $i] :
( ( ( ~ ( in @ SV53
@ ( dsetconstr @ SV15
@ ^ [SY350: $i] : ( SV38 @ SY350 ) ) ) )
= $true )
| ( ( in @ SV53 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(241,plain,
! [SV39: $i > $o,SV16: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV16 ) )
= $true )
| ( ( ~ ( SV39 @ SV54 )
| ( in @ SV54
@ ( dsetconstr @ SV16
@ ^ [SY352: $i] : ( SV39 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(242,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
| ~ ~ ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
| ( SV19 = SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(243,plain,
! [SV20: $i] :
( ( ! [SY297: $i > $o,SY298: $i] :
( ~ ( in @ SY298 @ SV20 )
| ~ ( SY297 @ SY298 )
| ( in @ SY298
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY297 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(244,plain,
! [SV20: $i] :
( ( ! [SY300: $i > $o,SY301: $i] :
( ~ ( in @ SY301 @ SV20 )
| ~ ( in @ SY301
@ ( dsetconstr @ SV20
@ ^ [SX3: $i] : ( SY300 @ SX3 ) ) )
| ( SY300 @ SY301 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(245,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ( ~ ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
| ~ ( ( SV55
!= ( sK18_SY70 @ SV55 @ SV21 ) ) ) ) )
= $true )
| ( ( ~ ( SV21 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(246,plain,
! [SV22: $i > $i > $o,SV41: $i] :
( ( ( ~ ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
| ~ ! [SY353: $i] :
( ~ ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) )
| ~ ( ( SY353
!= ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) ) ) )
| ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SY353 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(247,plain,
! [SV23: $i] :
( ( ! [SY310: $i] :
( ~ ( ~ ( in @ ( sK15_Xx @ SY310 @ SV23 ) @ SY310 )
| ~ ~ ( in @ ( sK15_Xx @ SY310 @ SV23 ) @ SV23 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY310 )
| ~ ( ~ ! [SY312: $i] :
( ~ ( in @ SY312 @ ( sK11_B @ SV23 ) )
| ! [SY313: $i] :
( ~ ( in @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK13_SY253 @ SY310 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SY310 @ SV23 ) @ SY312 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SY310 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SY310 @ SV23 ) @ SY310 ) )
| ~ ! [SY314: $i] :
( ~ ( in @ SY314 @ ( sK13_SY253 @ SY310 @ SV23 ) )
| ~ ( in @ SY314 @ SY310 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(248,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY315: $i,SY316: $i] :
( ~ ( in @ SY315 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SY316 @ ( sK11_B @ SV23 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY315 )
| ( in @ SX3 @ SY316 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY316 )
| ( in @ SX3 @ SY315 ) ) )
| ~ ~ ( ~ ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(249,plain,
! [SV24: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV42 )
| ~ ~ ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV24 ) )
= $false )
| ( ( in @ SV42 @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(250,plain,
! [SV56: $i,SV25: $i > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK20_SY83 @ SV56 @ SV25 ) )
| ~ ( ( SV56
!= ( sK20_SY83 @ SV56 @ SV25 ) ) ) ) )
= $true )
| ( ( ~ ( SV25 @ SV56 ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(251,plain,
! [SV26: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) )
| ~ ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) ) )
= $false )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(252,plain,
! [SV27: $i] :
( ( ! [SY326: $i,SY327: $i] :
( ~ ( in @ SY327 @ ( setadjoin @ SV27 @ SY326 ) )
| ( SY327 = SV27 )
| ( in @ SY327 @ SY326 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(253,plain,
! [SV27: $i] :
( ( ~ ( ~ ! [SY328: $i,SY329: $i] :
( ( SY329 != SV27 )
| ( in @ SY329 @ ( setadjoin @ SV27 @ SY328 ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ SY331 @ SY330 )
| ( in @ SY331 @ ( setadjoin @ SV27 @ SY330 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(254,plain,
! [SV28: $i,SV57: $i] :
( ( ( in @ SV57 @ SV28 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK10_B @ SV28 ) @ SV28 )
| ~ ! [SY333: $i] :
( ~ ( in @ SY333 @ ( sK10_B @ SV28 ) )
| ~ ( in @ SY333 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(255,plain,
! [SV29: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV29 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV29 ) @ SV29 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(256,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV58 = SV30 )
| ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV58 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY371: $o] :
( ~ SY371
| ( in @ SV58 @ SV44 )
| SY371 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(257,plain,
! [SV59: $i,SV31: $i > $o] :
( ( ( ~ ( ~ ( SV31 @ ( sK16_SY53 @ SV59 @ SV31 ) )
| ~ ( ( SV59
!= ( sK16_SY53 @ SV59 @ SV31 ) ) ) ) )
= $true )
| ( ( ~ ( SV31 @ SV59 ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(258,plain,
! [SV61: $i] :
( ( ! [SY373: $i] :
( ! [SY374: $i] :
( ~ ( in @ SY373 @ SY374 )
| ~ ( in @ SY374 @ SV61 ) )
| ( in @ SY373 @ ( setunion @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(259,plain,
! [SV62: $i] :
( ( ! [SY375: $i] :
( ~ ( in @ SY375 @ ( setunion @ SV62 ) )
| ~ ( ~ ( in @ SY375 @ ( sK4_B @ SY375 @ SV62 ) )
| ~ ( in @ ( sK4_B @ SY375 @ SV62 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(260,plain,
! [SV63: $i] :
( ( ! [SY376: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SY376 @ SV63 ) @ SY376 )
| ~ ~ ( in @ ( sK3_Xx @ SY376 @ SV63 ) @ SV63 ) )
| ( in @ SY376 @ ( powerset @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(261,plain,
! [SV64: $i] :
( ( ! [SY377: $i] :
( ~ ( in @ SY377 @ ( powerset @ SV64 ) )
| ! [SY378: $i] :
( ~ ( in @ SY378 @ SY377 )
| ( in @ SY378 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(262,plain,
! [SV32: $i,SV3: $i,SV45: $i] :
( ( ( in @ SV45 @ ( setadjoin @ SV3 @ SV32 ) )
= $false )
| ( ( ( SV45 = SV3 )
| ( in @ SV45 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(263,plain,
! [SV4: $i,SV33: $i,SV46: $i] :
( ( ( in @ SV46 @ SV33 )
= $false )
| ( ( in @ SV46 @ ( setadjoin @ SV4 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(264,plain,
! [SV47: $i,SV6: $i] :
( ( ( SV6 = emptyset )
= $false )
| ( ( in @ SV47 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(265,plain,
! [SV35: $i > $o,SV7: $i,SV48: $i] :
( ( ( in @ SV48 @ SV7 )
= $false )
| ( ( ~ ( SV35 @ SV48 )
| ( ( dsetconstr @ SV7
@ ^ [SY346: $i] : ( SV35 @ SY346 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(266,plain,
! [SV37: $i > $o,SV14: $i,SV52: $i] :
( ( ( in @ SV52
@ ( dsetconstr @ SV14
@ ^ [SY348: $i] : ( SV37 @ SY348 ) ) )
= $false )
| ( ( SV37 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(267,plain,
! [SV38: $i > $o,SV15: $i,SV53: $i] :
( ( ( in @ SV53
@ ( dsetconstr @ SV15
@ ^ [SY350: $i] : ( SV38 @ SY350 ) ) )
= $false )
| ( ( in @ SV53 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(268,plain,
! [SV39: $i > $o,SV16: $i,SV54: $i] :
( ( ( in @ SV54 @ SV16 )
= $false )
| ( ( ~ ( SV39 @ SV54 )
| ( in @ SV54
@ ( dsetconstr @ SV16
@ ^ [SY352: $i] : ( SV39 @ SY352 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(269,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
| ( SV19 = SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(270,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ~ ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
| ( SV19 = SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(271,plain,
! [SV65: $i > $o,SV20: $i] :
( ( ! [SY379: $i] :
( ~ ( in @ SY379 @ SV20 )
| ~ ( SV65 @ SY379 )
| ( in @ SY379
@ ( dsetconstr @ SV20
@ ^ [SY380: $i] : ( SV65 @ SY380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(272,plain,
! [SV66: $i > $o,SV20: $i] :
( ( ! [SY381: $i] :
( ~ ( in @ SY381 @ SV20 )
| ~ ( in @ SY381
@ ( dsetconstr @ SV20
@ ^ [SY382: $i] : ( SV66 @ SY382 ) ) )
| ( SV66 @ SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(273,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
| ~ ( ( SV55
!= ( sK18_SY70 @ SV55 @ SV21 ) ) ) )
= $false )
| ( ( ~ ( SV21 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(274,plain,
! [SV22: $i > $i > $o,SV41: $i] :
( ( ( ~ ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 ) )
= $false )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(275,plain,
! [SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ! [SY353: $i] :
( ~ ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) )
| ~ ( ( SY353
!= ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) ) ) )
| ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SY353 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(276,plain,
! [SV23: $i,SV67: $i] :
( ( ~ ( ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
| ~ ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 ) )
| ! [SY383: $i] :
~ ( in @ SY383 @ SV67 )
| ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(277,plain,
! [SV23: $i] :
( ( ~ ! [SY315: $i,SY316: $i] :
( ~ ( in @ SY315 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SY316 @ ( sK11_B @ SV23 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY315 )
| ( in @ SX3 @ SY316 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY316 )
| ( in @ SX3 @ SY315 ) ) )
| ~ ~ ( ~ ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(278,plain,
! [SV24: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV42 ) )
= $false )
| ( ( in @ SV42 @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(279,plain,
! [SV24: $i,SV42: $i] :
( ( ( ~ ~ ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV24 ) )
= $false )
| ( ( in @ SV42 @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(280,plain,
! [SV56: $i,SV25: $i > $o] :
( ( ( ~ ( SV25 @ ( sK20_SY83 @ SV56 @ SV25 ) )
| ~ ( ( SV56
!= ( sK20_SY83 @ SV56 @ SV25 ) ) ) )
= $false )
| ( ( ~ ( SV25 @ SV56 ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(281,plain,
! [SV26: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) ) )
= $false )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(282,plain,
! [SV26: $i,SV43: $i] :
( ( ( ~ ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) ) )
= $false )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(283,plain,
! [SV68: $i,SV27: $i] :
( ( ! [SY387: $i] :
( ~ ( in @ SY387 @ ( setadjoin @ SV27 @ SV68 ) )
| ( SY387 = SV27 )
| ( in @ SY387 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(284,plain,
! [SV27: $i] :
( ( ~ ! [SY328: $i,SY329: $i] :
( ( SY329 != SV27 )
| ( in @ SY329 @ ( setadjoin @ SV27 @ SY328 ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ SY331 @ SY330 )
| ( in @ SY331 @ ( setadjoin @ SV27 @ SY330 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(285,plain,
! [SV57: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK10_B @ SV28 ) @ SV28 )
| ~ ! [SY333: $i] :
( ~ ( in @ SY333 @ ( sK10_B @ SV28 ) )
| ~ ( in @ SY333 @ SV28 ) ) )
= $false )
| ( ( in @ SV57 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(286,plain,
! [SV29: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_Xx @ SV29 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV29 ) @ SV29 ) ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(287,plain,
! [SV29: $i] :
( ( ( ~ ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(288,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( SV58 = SV30 )
| ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV58 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY371: $o] :
( ~ SY371
| ( in @ SV58 @ SV44 )
| SY371 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(289,plain,
! [SV59: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ ( sK16_SY53 @ SV59 @ SV31 ) )
| ~ ( ( SV59
!= ( sK16_SY53 @ SV59 @ SV31 ) ) ) )
= $false )
| ( ( ~ ( SV31 @ SV59 ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(290,plain,
! [SV61: $i,SV69: $i] :
( ( ! [SY388: $i] :
( ~ ( in @ SV69 @ SY388 )
| ~ ( in @ SY388 @ SV61 ) )
| ( in @ SV69 @ ( setunion @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(291,plain,
! [SV62: $i,SV70: $i] :
( ( ~ ( in @ SV70 @ ( setunion @ SV62 ) )
| ~ ( ~ ( in @ SV70 @ ( sK4_B @ SV70 @ SV62 ) )
| ~ ( in @ ( sK4_B @ SV70 @ SV62 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(292,plain,
! [SV63: $i,SV71: $i] :
( ( ~ ( ~ ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV71 )
| ~ ~ ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV63 ) )
| ( in @ SV71 @ ( powerset @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(293,plain,
! [SV64: $i,SV72: $i] :
( ( ~ ( in @ SV72 @ ( powerset @ SV64 ) )
| ! [SY389: $i] :
( ~ ( in @ SY389 @ SV72 )
| ( in @ SY389 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(294,plain,
! [SV32: $i,SV3: $i,SV45: $i] :
( ( ( SV45 = SV3 )
= $true )
| ( ( in @ SV45 @ SV32 )
= $true )
| ( ( in @ SV45 @ ( setadjoin @ SV3 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(295,plain,
! [SV7: $i,SV48: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ SV48 ) )
= $true )
| ( ( ( dsetconstr @ SV7
@ ^ [SY346: $i] : ( SV35 @ SY346 ) )
!= emptyset )
= $true )
| ( ( in @ SV48 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(296,plain,
! [SV16: $i,SV54: $i,SV39: $i > $o] :
( ( ( ~ ( SV39 @ SV54 ) )
= $true )
| ( ( in @ SV54
@ ( dsetconstr @ SV16
@ ^ [SY352: $i] : ( SV39 @ SY352 ) ) )
= $true )
| ( ( in @ SV54 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(297,plain,
! [SV19: $i,SV40: $i] :
( ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
| ( SV19 = SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(298,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
| ( SV19 = SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(299,plain,
! [SV65: $i > $o,SV20: $i,SV73: $i] :
( ( ~ ( in @ SV73 @ SV20 )
| ~ ( SV65 @ SV73 )
| ( in @ SV73
@ ( dsetconstr @ SV20
@ ^ [SY380: $i] : ( SV65 @ SY380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(300,plain,
! [SV66: $i > $o,SV20: $i,SV74: $i] :
( ( ~ ( in @ SV74 @ SV20 )
| ~ ( in @ SV74
@ ( dsetconstr @ SV20
@ ^ [SY382: $i] : ( SV66 @ SY382 ) ) )
| ( SV66 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(301,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) ) )
= $false )
| ( ( ~ ( SV21 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(302,plain,
! [SV21: $i > $o,SV55: $i] :
( ( ( ~ ( ( SV55
!= ( sK18_SY70 @ SV55 @ SV21 ) ) ) )
= $false )
| ( ( ~ ( SV21 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(303,plain,
! [SV22: $i > $i > $o,SV41: $i] :
( ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(304,plain,
! [SV41: $i,SV22: $i > $i > $o] :
( ( ( ! [SY353: $i] :
( ~ ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) )
| ~ ( ( SY353
!= ( sK9_SY248 @ SY353 @ SV41 @ SV22 ) ) ) )
| ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SY353 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(305,plain,
! [SV23: $i,SV67: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
| ~ ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 ) )
| ! [SY383: $i] :
~ ( in @ SY383 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(306,plain,
! [SV23: $i] :
( ( ~ ! [SY315: $i,SY316: $i] :
( ~ ( in @ SY315 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SY316 @ ( sK11_B @ SV23 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY315 )
| ( in @ SX3 @ SY316 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY316 )
| ( in @ SX3 @ SY315 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(307,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(308,plain,
! [SV24: $i,SV42: $i] :
( ( ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV42 )
= $true )
| ( ( in @ SV42 @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(309,plain,
! [SV24: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV24 ) )
= $true )
| ( ( in @ SV42 @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(310,plain,
! [SV56: $i,SV25: $i > $o] :
( ( ( ~ ( SV25 @ ( sK20_SY83 @ SV56 @ SV25 ) ) )
= $false )
| ( ( ~ ( SV25 @ SV56 ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(311,plain,
! [SV25: $i > $o,SV56: $i] :
( ( ( ~ ( ( SV56
!= ( sK20_SY83 @ SV56 @ SV25 ) ) ) )
= $false )
| ( ( ~ ( SV25 @ SV56 ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(312,plain,
! [SV26: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) )
= $true )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(313,plain,
! [SV26: $i,SV43: $i] :
( ( ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
| ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) )
= $true )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(314,plain,
! [SV68: $i,SV27: $i,SV75: $i] :
( ( ~ ( in @ SV75 @ ( setadjoin @ SV27 @ SV68 ) )
| ( SV75 = SV27 )
| ( in @ SV75 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(315,plain,
! [SV27: $i] :
( ( ~ ! [SY328: $i,SY329: $i] :
( ( SY329 != SV27 )
| ( in @ SY329 @ ( setadjoin @ SV27 @ SY328 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(316,plain,
! [SV27: $i] :
( ( ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ SY331 @ SY330 )
| ( in @ SY331 @ ( setadjoin @ SV27 @ SY330 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(317,plain,
! [SV57: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK10_B @ SV28 ) @ SV28 ) )
= $false )
| ( ( in @ SV57 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(318,plain,
! [SV57: $i,SV28: $i] :
( ( ( ~ ! [SY333: $i] :
( ~ ( in @ SY333 @ ( sK10_B @ SV28 ) )
| ~ ( in @ SY333 @ SV28 ) ) )
= $false )
| ( ( in @ SV57 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(319,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_Xx @ SV29 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV29 ) @ SV29 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(320,plain,
! [SV29: $i] :
( ( ( ~ ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(321,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ( ( SV58 = SV30 )
| ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV58 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY371: $o] :
( ~ SY371
| ( in @ SV58 @ SV44 )
| SY371 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(322,plain,
! [SV59: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ ( sK16_SY53 @ SV59 @ SV31 ) ) )
= $false )
| ( ( ~ ( SV31 @ SV59 ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(323,plain,
! [SV31: $i > $o,SV59: $i] :
( ( ( ~ ( ( SV59
!= ( sK16_SY53 @ SV59 @ SV31 ) ) ) )
= $false )
| ( ( ~ ( SV31 @ SV59 ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(324,plain,
! [SV61: $i,SV69: $i] :
( ( ( ! [SY388: $i] :
( ~ ( in @ SV69 @ SY388 )
| ~ ( in @ SY388 @ SV61 ) ) )
= $true )
| ( ( in @ SV69 @ ( setunion @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(325,plain,
! [SV62: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ ( setunion @ SV62 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV70 @ ( sK4_B @ SV70 @ SV62 ) )
| ~ ( in @ ( sK4_B @ SV70 @ SV62 ) @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(326,plain,
! [SV63: $i,SV71: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV71 )
| ~ ~ ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( in @ SV71 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(327,plain,
! [SV64: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( ! [SY389: $i] :
( ~ ( in @ SY389 @ SV72 )
| ( in @ SY389 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(328,plain,
! [SV7: $i,SV48: $i,SV35: $i > $o] :
( ( ( SV35 @ SV48 )
= $false )
| ( ( ( dsetconstr @ SV7
@ ^ [SY346: $i] : ( SV35 @ SY346 ) )
!= emptyset )
= $true )
| ( ( in @ SV48 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(329,plain,
! [SV16: $i,SV54: $i,SV39: $i > $o] :
( ( ( SV39 @ SV54 )
= $false )
| ( ( in @ SV54
@ ( dsetconstr @ SV16
@ ^ [SY352: $i] : ( SV39 @ SY352 ) ) )
= $true )
| ( ( in @ SV54 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(330,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) ) )
= $true )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(331,plain,
! [SV19: $i,SV40: $i] :
( ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
| ( SV19 = SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(332,plain,
! [SV65: $i > $o,SV20: $i,SV73: $i] :
( ( ( ~ ( in @ SV73 @ SV20 ) )
= $true )
| ( ( ~ ( SV65 @ SV73 )
| ( in @ SV73
@ ( dsetconstr @ SV20
@ ^ [SY380: $i] : ( SV65 @ SY380 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(333,plain,
! [SV66: $i > $o,SV20: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ SV20 ) )
= $true )
| ( ( ~ ( in @ SV74
@ ( dsetconstr @ SV20
@ ^ [SY382: $i] : ( SV66 @ SY382 ) ) )
| ( SV66 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(334,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( ~ ( SV21 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(335,plain,
! [SV21: $i > $o,SV55: $i] :
( ( ( SV55
!= ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( ~ ( SV21 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(336,plain,
! [SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(337,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
| ~ ( ( SV76
!= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) ) ) )
| ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(338,plain,
! [SV23: $i,SV67: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
| ~ ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( ! [SY383: $i] :
~ ( in @ SY383 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(339,plain,
! [SV23: $i] :
( ( ! [SY315: $i,SY316: $i] :
( ~ ( in @ SY315 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SY316 @ ( sK11_B @ SV23 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY315 )
| ( in @ SX3 @ SY316 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY316 )
| ( in @ SX3 @ SY315 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(340,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(341,plain,
! [SV24: $i,SV42: $i] :
( ( ( in @ ( sK26_Xx @ SV42 @ SV24 ) @ SV24 )
= $false )
| ( ( in @ SV42 @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(342,plain,
! [SV56: $i,SV25: $i > $o] :
( ( ( SV25 @ ( sK20_SY83 @ SV56 @ SV25 ) )
= $true )
| ( ( ~ ( SV25 @ SV56 ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(343,plain,
! [SV25: $i > $o,SV56: $i] :
( ( ( SV56
!= ( sK20_SY83 @ SV56 @ SV25 ) )
= $true )
| ( ( ~ ( SV25 @ SV56 ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(344,plain,
! [SV26: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 ) )
= $true )
| ( ( ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) )
= $true )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(345,plain,
! [SV26: $i,SV43: $i] :
( ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
= $true )
| ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 )
= $true )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(346,plain,
! [SV68: $i,SV27: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ ( setadjoin @ SV27 @ SV68 ) ) )
= $true )
| ( ( ( SV75 = SV27 )
| ( in @ SV75 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(347,plain,
! [SV27: $i] :
( ( ! [SY328: $i,SY329: $i] :
( ( SY329 != SV27 )
| ( in @ SY329 @ ( setadjoin @ SV27 @ SY328 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(348,plain,
! [SV27: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ~ ( in @ SY331 @ SY330 )
| ( in @ SY331 @ ( setadjoin @ SV27 @ SY330 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(349,plain,
! [SV57: $i,SV28: $i] :
( ( ( in @ ( sK10_B @ SV28 ) @ SV28 )
= $true )
| ( ( in @ SV57 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(350,plain,
! [SV57: $i,SV28: $i] :
( ( ( ! [SY333: $i] :
( ~ ( in @ SY333 @ ( sK10_B @ SV28 ) )
| ~ ( in @ SY333 @ SV28 ) ) )
= $true )
| ( ( in @ SV57 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(351,plain,
! [SV29: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV29 ) @ omega )
| ~ ( in @ ( sK5_Xx @ SV29 ) @ SV29 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(352,plain,
! [SV29: $i] :
( ( ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 )
= $false )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(353,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ( ( SV58 = SV30 )
| ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV58 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(354,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ! [SY371: $o] :
( ~ SY371
| ( in @ SV58 @ SV44 )
| SY371 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(355,plain,
! [SV59: $i,SV31: $i > $o] :
( ( ( SV31 @ ( sK16_SY53 @ SV59 @ SV31 ) )
= $true )
| ( ( ~ ( SV31 @ SV59 ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(356,plain,
! [SV31: $i > $o,SV59: $i] :
( ( ( SV59
!= ( sK16_SY53 @ SV59 @ SV31 ) )
= $true )
| ( ( ~ ( SV31 @ SV59 ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(357,plain,
! [SV61: $i,SV77: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ SV77 )
| ~ ( in @ SV77 @ SV61 ) )
= $true )
| ( ( in @ SV69 @ ( setunion @ SV61 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(358,plain,
! [SV62: $i,SV70: $i] :
( ( ( in @ SV70 @ ( setunion @ SV62 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV70 @ ( sK4_B @ SV70 @ SV62 ) )
| ~ ( in @ ( sK4_B @ SV70 @ SV62 ) @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(359,plain,
! [SV63: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV71 )
| ~ ~ ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ SV71 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(360,plain,
! [SV64: $i,SV72: $i] :
( ( ( in @ SV72 @ ( powerset @ SV64 ) )
= $false )
| ( ( ! [SY389: $i] :
( ~ ( in @ SY389 @ SV72 )
| ( in @ SY389 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(361,plain,
! [SV48: $i,SV35: $i > $o,SV7: $i] :
( ( ( ( dsetconstr @ SV7
@ ^ [SY346: $i] : ( SV35 @ SY346 ) )
= emptyset )
= $false )
| ( ( SV35 @ SV48 )
= $false )
| ( ( in @ SV48 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(362,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
= $false )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(363,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) ) )
= $true )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(364,plain,
! [SV65: $i > $o,SV20: $i,SV73: $i] :
( ( ( in @ SV73 @ SV20 )
= $false )
| ( ( ~ ( SV65 @ SV73 )
| ( in @ SV73
@ ( dsetconstr @ SV20
@ ^ [SY380: $i] : ( SV65 @ SY380 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(365,plain,
! [SV66: $i > $o,SV20: $i,SV74: $i] :
( ( ( in @ SV74 @ SV20 )
= $false )
| ( ( ~ ( in @ SV74
@ ( dsetconstr @ SV20
@ ^ [SY382: $i] : ( SV66 @ SY382 ) ) )
| ( SV66 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(366,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( SV21 @ SV55 )
= $false )
| ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(367,plain,
! [SV21: $i > $o,SV55: $i] :
( ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( ~ ( SV21 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(368,plain,
! [SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(369,plain,
! [SV22: $i > $i > $o,SV41: $i] :
( ( ( ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(370,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
| ~ ( ( SV76
!= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) ) ) ) )
= $true )
| ( ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(371,plain,
! [SV23: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
| ~ ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 ) )
= $false )
| ( ( ! [SY383: $i] :
~ ( in @ SY383 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(372,plain,
! [SV23: $i,SV78: $i] :
( ( ! [SY392: $i] :
( ~ ( in @ SV78 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SY392 @ ( sK11_B @ SV23 ) )
| ! [SY393: $i] :
( ~ ( in @ SY393 @ SV78 )
| ( in @ SY393 @ SY392 ) )
| ! [SY394: $i] :
( ~ ( in @ SY394 @ SY392 )
| ( in @ SY394 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(373,plain,
! [SV23: $i] :
( ( ~ ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(374,plain,
! [SV56: $i,SV25: $i > $o] :
( ( ( SV25 @ SV56 )
= $false )
| ( ( SV25 @ ( sK20_SY83 @ SV56 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(375,plain,
! [SV25: $i > $o,SV56: $i] :
( ( ( SV56
= ( sK20_SY83 @ SV56 @ SV25 ) )
= $false )
| ( ( ~ ( SV25 @ SV56 ) )
= $true )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(376,plain,
! [SV26: $i,SV43: $i] :
( ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
= $false )
| ( ( ~ ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 ) )
= $true )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(377,plain,
! [SV68: $i,SV27: $i,SV75: $i] :
( ( ( in @ SV75 @ ( setadjoin @ SV27 @ SV68 ) )
= $false )
| ( ( ( SV75 = SV27 )
| ( in @ SV75 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(378,plain,
! [SV79: $i,SV27: $i] :
( ( ! [SY395: $i] :
( ( SY395 != SV27 )
| ( in @ SY395 @ ( setadjoin @ SV27 @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(379,plain,
! [SV27: $i,SV80: $i] :
( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ SV80 )
| ( in @ SY396 @ ( setadjoin @ SV27 @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(380,plain,
! [SV57: $i,SV28: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ ( sK10_B @ SV28 ) )
| ~ ( in @ SV81 @ SV28 ) )
= $true )
| ( ( in @ SV57 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(381,plain,
! [SV29: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV29 ) @ omega ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(382,plain,
! [SV29: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV29 ) @ SV29 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(383,plain,
! [SV29: $i] :
( ( ( in @ emptyset @ SV29 )
= $false )
| ( ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 )
= $false )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(384,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ ( ~ ( ( SV58 = SV30 )
| ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV58 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(385,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( ~ ( ~ ! [SY371: $o] :
( ~ SY371
| ( in @ SV58 @ SV44 )
| SY371 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(386,plain,
! [SV59: $i,SV31: $i > $o] :
( ( ( SV31 @ SV59 )
= $false )
| ( ( SV31 @ ( sK16_SY53 @ SV59 @ SV31 ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(387,plain,
! [SV31: $i > $o,SV59: $i] :
( ( ( SV59
= ( sK16_SY53 @ SV59 @ SV31 ) )
= $false )
| ( ( ~ ( SV31 @ SV59 ) )
= $true )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(388,plain,
! [SV61: $i,SV77: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ SV77 ) )
= $true )
| ( ( ~ ( in @ SV77 @ SV61 ) )
= $true )
| ( ( in @ SV69 @ ( setunion @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(389,plain,
! [SV62: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ ( sK4_B @ SV70 @ SV62 ) )
| ~ ( in @ ( sK4_B @ SV70 @ SV62 ) @ SV62 ) )
= $false )
| ( ( in @ SV70 @ ( setunion @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(390,plain,
! [SV63: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV71 ) )
= $false )
| ( ( in @ SV71 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(391,plain,
! [SV63: $i,SV71: $i] :
( ( ( ~ ~ ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ SV71 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(392,plain,
! [SV64: $i,SV72: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ SV72 )
| ( in @ SV82 @ SV64 ) )
= $true )
| ( ( in @ SV72 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(393,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 ) )
= $false )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(394,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
= $false )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(395,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
| ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
= $false )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(396,plain,
! [SV20: $i,SV73: $i,SV65: $i > $o] :
( ( ( ~ ( SV65 @ SV73 ) )
= $true )
| ( ( in @ SV73
@ ( dsetconstr @ SV20
@ ^ [SY380: $i] : ( SV65 @ SY380 ) ) )
= $true )
| ( ( in @ SV73 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(397,plain,
! [SV66: $i > $o,SV20: $i,SV74: $i] :
( ( ( ~ ( in @ SV74
@ ( dsetconstr @ SV20
@ ^ [SY382: $i] : ( SV66 @ SY382 ) ) ) )
= $true )
| ( ( SV66 @ SV74 )
= $true )
| ( ( in @ SV74 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(398,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(399,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( SV21 @ SV55 )
= $false )
| ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( ~ ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(400,plain,
! [SV41: $i,SV22: $i > $i > $o] :
( ( ( ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(401,plain,
! [SV22: $i > $i > $o,SV41: $i] :
( ( ( ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(402,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
| ~ ( ( SV76
!= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) ) ) )
= $false )
| ( ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(403,plain,
! [SV23: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 ) )
= $false )
| ( ( ! [SY383: $i] :
~ ( in @ SY383 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(404,plain,
! [SV23: $i,SV67: $i] :
( ( ( ~ ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 ) )
= $false )
| ( ( ! [SY383: $i] :
~ ( in @ SY383 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(405,plain,
! [SV83: $i,SV23: $i,SV78: $i] :
( ( ~ ( in @ SV78 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SV83 @ ( sK11_B @ SV23 ) )
| ! [SY397: $i] :
( ~ ( in @ SY397 @ SV78 )
| ( in @ SY397 @ SV83 ) )
| ! [SY398: $i] :
( ~ ( in @ SY398 @ SV83 )
| ( in @ SY398 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(406,plain,
! [SV23: $i] :
( ( ~ ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(407,plain,
! [SV23: $i] :
( ( ~ ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(408,plain,
! [SV56: $i,SV25: $i > $o] :
( ( ( SV25 @ SV56 )
= $false )
| ( ( SV56
= ( sK20_SY83 @ SV56 @ SV25 ) )
= $false )
| ( ( SV25 @ ( sK19_Xx @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(409,plain,
! [SV26: $i,SV43: $i] :
( ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV43 )
= $false )
| ( ( in @ ( sK2_Xx @ SV43 @ SV26 ) @ SV26 )
= $false )
| ( ( SV26 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(410,plain,
! [SV68: $i,SV27: $i,SV75: $i] :
( ( ( SV75 = SV27 )
= $true )
| ( ( in @ SV75 @ SV68 )
= $true )
| ( ( in @ SV75 @ ( setadjoin @ SV27 @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(411,plain,
! [SV79: $i,SV27: $i,SV84: $i] :
( ( ( SV84 != SV27 )
| ( in @ SV84 @ ( setadjoin @ SV27 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(412,plain,
! [SV27: $i,SV80: $i,SV85: $i] :
( ( ~ ( in @ SV85 @ SV80 )
| ( in @ SV85 @ ( setadjoin @ SV27 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(413,plain,
! [SV57: $i,SV28: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ ( sK10_B @ SV28 ) ) )
= $true )
| ( ( ~ ( in @ SV81 @ SV28 ) )
= $true )
| ( ( in @ SV57 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(414,plain,
! [SV29: $i] :
( ( ( in @ ( sK5_Xx @ SV29 ) @ omega )
= $true )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(415,plain,
! [SV29: $i] :
( ( ( in @ ( sK5_Xx @ SV29 ) @ SV29 )
= $true )
| ( ( ~ ( in @ emptyset @ SV29 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(416,plain,
! [SV29: $i,SV86: $i] :
( ( ( ~ ( in @ SV86 @ omega )
| ( in @ SV86 @ SV29 ) )
= $true )
| ( ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 )
= $false )
| ( ( in @ emptyset @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(417,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ ( ( SV58 = SV30 )
| ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV58 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(418,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( ~ ! [SY371: $o] :
( ~ SY371
| ( in @ SV58 @ SV44 )
| SY371 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(419,plain,
! [SV59: $i,SV31: $i > $o] :
( ( ( SV31 @ SV59 )
= $false )
| ( ( SV59
= ( sK16_SY53 @ SV59 @ SV31 ) )
= $false )
| ( ( SV31
@ ( descr
@ ^ [SY342: $i] : ( SV31 @ SY342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(420,plain,
! [SV61: $i,SV77: $i,SV69: $i] :
( ( ( in @ SV69 @ SV77 )
= $false )
| ( ( ~ ( in @ SV77 @ SV61 ) )
= $true )
| ( ( in @ SV69 @ ( setunion @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(421,plain,
! [SV62: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ ( sK4_B @ SV70 @ SV62 ) ) )
= $false )
| ( ( in @ SV70 @ ( setunion @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(422,plain,
! [SV62: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK4_B @ SV70 @ SV62 ) @ SV62 ) )
= $false )
| ( ( in @ SV70 @ ( setunion @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(423,plain,
! [SV63: $i,SV71: $i] :
( ( ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV71 )
= $true )
| ( ( in @ SV71 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(424,plain,
! [SV63: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV63 ) )
= $true )
| ( ( in @ SV71 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(425,plain,
! [SV64: $i,SV72: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ SV72 ) )
= $true )
| ( ( in @ SV82 @ SV64 )
= $true )
| ( ( in @ SV72 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(426,plain,
! [SV19: $i,SV40: $i] :
( ( ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
= $true )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(427,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
= $true )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(428,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 ) )
= $false )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(429,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
= $false )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(430,plain,
! [SV20: $i,SV73: $i,SV65: $i > $o] :
( ( ( SV65 @ SV73 )
= $false )
| ( ( in @ SV73
@ ( dsetconstr @ SV20
@ ^ [SY380: $i] : ( SV65 @ SY380 ) ) )
= $true )
| ( ( in @ SV73 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(431,plain,
! [SV66: $i > $o,SV20: $i,SV74: $i] :
( ( ( in @ SV74
@ ( dsetconstr @ SV20
@ ^ [SY382: $i] : ( SV66 @ SY382 ) ) )
= $false )
| ( ( SV66 @ SV74 )
= $true )
| ( ( in @ SV74 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(432,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) ) )
= $false )
| ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(433,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(434,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) )
| ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) )
= $false )
| ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(435,plain,
! [SV41: $i,SV87: $i,SV22: $i > $i > $o] :
( ( ( ! [SY399: $i] :
( ~ ( SV22 @ SY399 @ SV87 )
| ~ ( in @ SY399 @ SV41 ) )
| ( in @ SV87 @ ( sK6_B @ SV41 @ SV22 ) ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(436,plain,
! [SV22: $i > $i > $o,SV41: $i,SV88: $i] :
( ( ( ~ ( in @ SV88 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV88 )
| ~ ( in @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV41 ) ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(437,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) ) )
= $false )
| ( ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(438,plain,
! [SV22: $i > $i > $o,SV41: $i,SV76: $i] :
( ( ( ~ ( ( SV76
!= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) ) ) )
= $false )
| ( ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(439,plain,
! [SV23: $i,SV67: $i] :
( ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( ! [SY383: $i] :
~ ( in @ SY383 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(440,plain,
! [SV23: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 ) )
= $true )
| ( ( ! [SY383: $i] :
~ ( in @ SY383 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(441,plain,
! [SV83: $i,SV23: $i,SV78: $i] :
( ( ( ~ ( in @ SV78 @ ( sK11_B @ SV23 ) )
| ~ ( in @ SV83 @ ( sK11_B @ SV23 ) ) )
= $true )
| ( ( ! [SY397: $i] :
( ~ ( in @ SY397 @ SV78 )
| ( in @ SY397 @ SV83 ) )
| ! [SY398: $i] :
( ~ ( in @ SY398 @ SV83 )
| ( in @ SY398 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(442,plain,
! [SV23: $i] :
( ( ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK11_B @ SV23 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SY319 )
| ( in @ SY320 @ SV23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(443,plain,
! [SV23: $i] :
( ( ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ SV23 )
| ~ ( in @ SY322 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ~ ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) )
| ~ ( ( in @ SY321 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) )
| ( in @ SY322 @ ( sK12_SY266 @ SY322 @ SY321 @ SV23 ) ) ) ) )
| ( SY321 = SY322 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(444,plain,
! [SV79: $i,SV27: $i,SV84: $i] :
( ( ( SV84 != SV27 )
= $true )
| ( ( in @ SV84 @ ( setadjoin @ SV27 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(445,plain,
! [SV27: $i,SV80: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ SV80 ) )
= $true )
| ( ( in @ SV85 @ ( setadjoin @ SV27 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(446,plain,
! [SV57: $i,SV28: $i,SV81: $i] :
( ( ( in @ SV81 @ ( sK10_B @ SV28 ) )
= $false )
| ( ( ~ ( in @ SV81 @ SV28 ) )
= $true )
| ( ( in @ SV57 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(447,plain,
! [SV29: $i] :
( ( ( in @ emptyset @ SV29 )
= $false )
| ( ( in @ ( sK5_Xx @ SV29 ) @ omega )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(448,plain,
! [SV29: $i] :
( ( ( in @ emptyset @ SV29 )
= $false )
| ( ( in @ ( sK5_Xx @ SV29 ) @ SV29 )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( in @ SY334 @ omega )
| ( in @ SY334 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(449,plain,
! [SV29: $i,SV86: $i] :
( ( ( ~ ( in @ SV86 @ omega ) )
= $true )
| ( ( in @ SV86 @ SV29 )
= $true )
| ( ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 )
= $false )
| ( ( in @ emptyset @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(450,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ ( ( SV58 = SV30 )
| ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(451,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ ( ( SV58 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(452,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( ~ ! [SY371: $o] :
( ~ SY371
| ( in @ SV58 @ SV44 )
| SY371 ) )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(453,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(454,plain,
! [SV69: $i,SV61: $i,SV77: $i] :
( ( ( in @ SV77 @ SV61 )
= $false )
| ( ( in @ SV69 @ SV77 )
= $false )
| ( ( in @ SV69 @ ( setunion @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(455,plain,
! [SV62: $i,SV70: $i] :
( ( ( in @ SV70 @ ( sK4_B @ SV70 @ SV62 ) )
= $true )
| ( ( in @ SV70 @ ( setunion @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(456,plain,
! [SV62: $i,SV70: $i] :
( ( ( in @ ( sK4_B @ SV70 @ SV62 ) @ SV62 )
= $true )
| ( ( in @ SV70 @ ( setunion @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(457,plain,
! [SV63: $i,SV71: $i] :
( ( ( in @ ( sK3_Xx @ SV71 @ SV63 ) @ SV63 )
= $false )
| ( ( in @ SV71 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(458,plain,
! [SV64: $i,SV72: $i,SV82: $i] :
( ( ( in @ SV82 @ SV72 )
= $false )
| ( ( in @ SV82 @ SV64 )
= $true )
| ( ( in @ SV72 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(459,plain,
! [SV19: $i,SV40: $i] :
( ( ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 )
= $false )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(460,plain,
! [SV19: $i,SV40: $i] :
( ( ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV40 )
= $true )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(461,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 ) )
= $true )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(462,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) ) )
= $true )
| ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(463,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( SV21 @ ( sK17_Xx @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(464,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) ) )
= $false )
| ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(465,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK17_Xx @ SV21 ) ) )
= $false )
| ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(466,plain,
! [SV41: $i,SV87: $i,SV22: $i > $i > $o] :
( ( ( ! [SY399: $i] :
( ~ ( SV22 @ SY399 @ SV87 )
| ~ ( in @ SY399 @ SV41 ) ) )
= $true )
| ( ( in @ SV87 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(467,plain,
! [SV22: $i > $i > $o,SV41: $i,SV88: $i] :
( ( ( ~ ( in @ SV88 @ ( sK6_B @ SV41 @ SV22 ) ) )
= $true )
| ( ( ~ ( ~ ( SV22 @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV88 )
| ~ ( in @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV41 ) ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(468,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(469,plain,
! [SV22: $i > $i > $o,SV41: $i,SV76: $i] :
( ( ( SV76
!= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(470,plain,
! [SV23: $i,SV67: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ SV67 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(471,plain,
! [SV23: $i,SV67: $i] :
( ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( ! [SY383: $i] :
~ ( in @ SY383 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(472,plain,
! [SV83: $i,SV23: $i,SV78: $i] :
( ( ( ~ ( in @ SV78 @ ( sK11_B @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ SV83 @ ( sK11_B @ SV23 ) ) )
= $true )
| ( ( ! [SY397: $i] :
( ~ ( in @ SY397 @ SV78 )
| ( in @ SY397 @ SV83 ) )
| ! [SY398: $i] :
( ~ ( in @ SY398 @ SV83 )
| ( in @ SY398 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(473,plain,
! [SV23: $i,SV90: $i] :
( ( ~ ( in @ SV90 @ ( sK11_B @ SV23 ) )
| ! [SY400: $i] :
( ~ ( in @ SY400 @ SV90 )
| ( in @ SY400 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(474,plain,
! [SV23: $i,SV91: $i] :
( ( ! [SY401: $i] :
( ~ ( in @ SV91 @ SV23 )
| ~ ( in @ SY401 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SY401 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SY401 @ SV91 @ SV23 ) )
| ~ ( in @ SY401 @ ( sK12_SY266 @ SY401 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SY401 @ SV91 @ SV23 ) )
| ( in @ SY401 @ ( sK12_SY266 @ SY401 @ SV91 @ SV23 ) ) ) ) )
| ( SV91 = SY401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(475,plain,
! [SV79: $i,SV27: $i,SV84: $i] :
( ( ( SV84 = SV27 )
= $false )
| ( ( in @ SV84 @ ( setadjoin @ SV27 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(476,plain,
! [SV27: $i,SV80: $i,SV85: $i] :
( ( ( in @ SV85 @ SV80 )
= $false )
| ( ( in @ SV85 @ ( setadjoin @ SV27 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(477,plain,
! [SV57: $i,SV28: $i,SV81: $i] :
( ( ( in @ SV81 @ SV28 )
= $false )
| ( ( in @ SV81 @ ( sK10_B @ SV28 ) )
= $false )
| ( ( in @ SV57 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(478,plain,
! [SV29: $i,SV92: $i] :
( ( ( ~ ( in @ SV92 @ omega )
| ( in @ SV92 @ SV29 ) )
= $true )
| ( ( in @ ( sK5_Xx @ SV29 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(479,plain,
! [SV29: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ omega )
| ( in @ SV93 @ SV29 ) )
= $true )
| ( ( in @ ( sK5_Xx @ SV29 ) @ SV29 )
= $true )
| ( ( in @ emptyset @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(480,plain,
! [SV29: $i,SV86: $i] :
( ( ( in @ SV86 @ omega )
= $false )
| ( ( in @ SV86 @ SV29 )
= $true )
| ( ( in @ ( setadjoin @ ( sK5_Xx @ SV29 ) @ ( sK5_Xx @ SV29 ) ) @ SV29 )
= $false )
| ( ( in @ emptyset @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(481,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ( SV58 = SV30 )
| ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(482,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ( SV58 = SV30 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(483,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( ! [SY371: $o] :
( ~ SY371
| ( in @ SV58 @ SV44 )
| SY371 ) )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(484,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(485,plain,
! [SV19: $i,SV40: $i] :
( ( ( in @ ( sK21_Xx @ SV40 @ SV19 ) @ SV19 )
= $false )
| ( ( SV19 = SV40 )
= $true )
| ( ( in @ ( sK22_Xx @ SV40 @ SV19 ) @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(486,plain,
! [SV55: $i,SV94: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV94 )
| ( ( sK17_Xx @ SV21 )
= SV94 ) )
= $true )
| ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(487,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( ! [SY304: $i] :
( ~ ( SV21 @ SY304 )
| ( ( sK17_Xx @ SV21 )
= SY304 ) ) )
= $true )
| ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(488,plain,
! [SV55: $i,SV21: $i > $o] :
( ( ( SV21 @ ( sK17_Xx @ SV21 ) )
= $true )
| ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(489,plain,
! [SV41: $i,SV87: $i,SV95: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ SV95 @ SV87 )
| ~ ( in @ SV95 @ SV41 ) )
= $true )
| ( ( in @ SV87 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(490,plain,
! [SV22: $i > $i > $o,SV41: $i,SV88: $i] :
( ( ( in @ SV88 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( ~ ( ~ ( SV22 @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV88 )
| ~ ( in @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV41 ) ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(491,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(492,plain,
! [SV22: $i > $i > $o,SV41: $i,SV76: $i] :
( ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( ~ ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(493,plain,
! [SV23: $i,SV67: $i,SV89: $i] :
( ( ( in @ SV89 @ SV67 )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(494,plain,
! [SV23: $i,SV67: $i,SV96: $i] :
( ( ( ~ ( in @ SV96 @ SV67 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(495,plain,
! [SV83: $i,SV23: $i,SV78: $i] :
( ( ( in @ SV78 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( ~ ( in @ SV83 @ ( sK11_B @ SV23 ) ) )
= $true )
| ( ( ! [SY397: $i] :
( ~ ( in @ SY397 @ SV78 )
| ( in @ SY397 @ SV83 ) )
| ! [SY398: $i] :
( ~ ( in @ SY398 @ SV83 )
| ( in @ SY398 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(496,plain,
! [SV23: $i,SV90: $i] :
( ( ( ~ ( in @ SV90 @ ( sK11_B @ SV23 ) ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( in @ SY400 @ SV90 )
| ( in @ SY400 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(497,plain,
! [SV97: $i,SV23: $i,SV91: $i] :
( ( ~ ( in @ SV91 @ SV23 )
| ~ ( in @ SV97 @ SV23 )
| ~ ( ~ ( in @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) ) )
| ( SV91 = SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(498,plain,
! [SV29: $i,SV92: $i] :
( ( ( ~ ( in @ SV92 @ omega ) )
= $true )
| ( ( in @ SV92 @ SV29 )
= $true )
| ( ( in @ ( sK5_Xx @ SV29 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(499,plain,
! [SV29: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ omega ) )
= $true )
| ( ( in @ SV93 @ SV29 )
= $true )
| ( ( in @ ( sK5_Xx @ SV29 ) @ SV29 )
= $true )
| ( ( in @ emptyset @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(500,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( SV58 = SV30 )
= $true )
| ( ( ( in @ SV58 @ SV44 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(501,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( SV58 = SV30 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(502,plain,
! [SV30: $i,SV44: $i,SV58: $i,SV98: $o] :
( ( ( ~ SV98
| ( in @ SV58 @ SV44 )
| SV98 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[483]) ).
thf(503,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( ~ $true
| ( in @ SV58 @ SV44 )
| $true )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[483]) ).
thf(504,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( ~ $false
| ( in @ SV58 @ SV44 )
| $false )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[483]) ).
thf(505,plain,
! [SV44: $i,SV30: $i,SV58: $i,SV99: $o] :
( ( ( ~ SV99
| ~ SV99
| SV99 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[484]) ).
thf(506,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[484]) ).
thf(507,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[484]) ).
thf(508,plain,
! [SV55: $i,SV94: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV94 ) )
= $true )
| ( ( ( sK17_Xx @ SV21 )
= SV94 )
= $true )
| ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(509,plain,
! [SV55: $i,SV100: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV100 )
| ( ( sK17_Xx @ SV21 )
= SV100 ) )
= $true )
| ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(510,plain,
! [SV41: $i,SV87: $i,SV95: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ SV95 @ SV87 ) )
= $true )
| ( ( ~ ( in @ SV95 @ SV41 ) )
= $true )
| ( ( in @ SV87 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(511,plain,
! [SV41: $i,SV88: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV88 )
| ~ ( in @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV41 ) )
= $false )
| ( ( in @ SV88 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(512,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(513,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( ~ ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(514,plain,
! [SV89: $i,SV67: $i,SV23: $i] :
( ( ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(515,plain,
! [SV23: $i,SV67: $i,SV96: $i] :
( ( ( in @ SV96 @ SV67 )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( ~ ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(516,plain,
! [SV78: $i,SV23: $i,SV83: $i] :
( ( ( in @ SV83 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ SV78 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( ! [SY397: $i] :
( ~ ( in @ SY397 @ SV78 )
| ( in @ SY397 @ SV83 ) )
| ! [SY398: $i] :
( ~ ( in @ SY398 @ SV83 )
| ( in @ SY398 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(517,plain,
! [SV23: $i,SV90: $i] :
( ( ( in @ SV90 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( ! [SY400: $i] :
( ~ ( in @ SY400 @ SV90 )
| ( in @ SY400 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(518,plain,
! [SV97: $i,SV23: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ SV23 )
| ~ ( in @ SV97 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) ) )
| ( SV91 = SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(519,plain,
! [SV29: $i,SV92: $i] :
( ( ( in @ SV92 @ omega )
= $false )
| ( ( in @ SV92 @ SV29 )
= $true )
| ( ( in @ ( sK5_Xx @ SV29 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(520,plain,
! [SV29: $i,SV93: $i] :
( ( ( in @ SV93 @ omega )
= $false )
| ( ( in @ SV93 @ SV29 )
= $true )
| ( ( in @ ( sK5_Xx @ SV29 ) @ SV29 )
= $true )
| ( ( in @ emptyset @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(521,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( in @ SV58 @ SV44 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(522,plain,
! [SV44: $i,SV30: $i,SV58: $i,SV101: $o] :
( ( ( ~ SV101
| SV101 )
= $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[501]) ).
thf(523,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[501]) ).
thf(524,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[501]) ).
thf(525,plain,
! [SV30: $i,SV44: $i,SV58: $i,SV98: $o] :
( ( ( ~ SV98 ) = $true )
| ( ( ( in @ SV58 @ SV44 )
| SV98 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(526,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV58 @ SV44 )
| $true )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(527,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV58 @ SV44 )
| $false )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(528,plain,
! [SV44: $i,SV30: $i,SV58: $i,SV99: $o] :
( ( ( ~ SV99 ) = $true )
| ( ( ~ SV99
| SV99 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(529,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(530,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(531,plain,
! [SV55: $i,SV94: $i,SV21: $i > $o] :
( ( ( SV21 @ SV94 )
= $false )
| ( ( ( sK17_Xx @ SV21 )
= SV94 )
= $true )
| ( ( SV21 @ ( sK18_SY70 @ SV55 @ SV21 ) )
= $true )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(532,plain,
! [SV55: $i,SV100: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV100 ) )
= $true )
| ( ( ( sK17_Xx @ SV21 )
= SV100 )
= $true )
| ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(533,plain,
! [SV41: $i,SV87: $i,SV95: $i,SV22: $i > $i > $o] :
( ( ( SV22 @ SV95 @ SV87 )
= $false )
| ( ( ~ ( in @ SV95 @ SV41 ) )
= $true )
| ( ( in @ SV87 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(534,plain,
! [SV41: $i,SV88: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV88 ) )
= $false )
| ( ( in @ SV88 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(535,plain,
! [SV22: $i > $i > $o,SV41: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV41 ) )
= $false )
| ( ( in @ SV88 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(536,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(537,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i] :
( ( ( ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(538,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) )
= $false )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(539,plain,
! [SV89: $i,SV67: $i,SV23: $i] :
( ( ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(540,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(541,plain,
! [SV96: $i,SV67: $i,SV23: $i] :
( ( ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(542,plain,
! [SV23: $i,SV83: $i,SV78: $i] :
( ( ( ! [SY397: $i] :
( ~ ( in @ SY397 @ SV78 )
| ( in @ SY397 @ SV83 ) ) )
= $true )
| ( ( ! [SY398: $i] :
( ~ ( in @ SY398 @ SV83 )
| ( in @ SY398 @ SV78 ) ) )
= $true )
| ( ( in @ SV78 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ SV83 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(543,plain,
! [SV23: $i,SV90: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV90 )
| ( in @ SV102 @ SV23 ) )
= $true )
| ( ( in @ SV90 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(544,plain,
! [SV97: $i,SV23: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV97 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) ) )
| ( SV91 = SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(545,plain,
! [SV30: $i,SV44: $i,SV58: $i,SV103: $o] :
( ( SV103 = $true )
| ( ( in @ SV58 @ SV44 )
= $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[521]) ).
thf(546,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( $true = $true )
| ( ( in @ SV58 @ SV44 )
= $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[521]) ).
thf(547,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( $false = $true )
| ( ( in @ SV58 @ SV44 )
= $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[521]) ).
thf(548,plain,
! [SV44: $i,SV30: $i,SV58: $i,SV101: $o] :
( ( ( ~ SV101 ) = $true )
| ( SV101 = $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(549,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(550,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(551,plain,
! [SV30: $i,SV44: $i,SV58: $i,SV98: $o] :
( ( SV98 = $false )
| ( ( ( in @ SV58 @ SV44 )
| SV98 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(552,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( $true = $false )
| ( ( ( in @ SV58 @ SV44 )
| $true )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(553,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( $false = $false )
| ( ( ( in @ SV58 @ SV44 )
| $false )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(554,plain,
! [SV44: $i,SV30: $i,SV58: $i,SV99: $o] :
( ( SV99 = $false )
| ( ( ~ SV99
| SV99 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(555,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(556,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(557,plain,
! [SV55: $i,SV100: $i,SV21: $i > $o] :
( ( ( SV21 @ SV100 )
= $false )
| ( ( ( sK17_Xx @ SV21 )
= SV100 )
= $true )
| ( ( SV55
= ( sK18_SY70 @ SV55 @ SV21 ) )
= $false )
| ( ( SV21 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(558,plain,
! [SV87: $i,SV22: $i > $i > $o,SV41: $i,SV95: $i] :
( ( ( in @ SV95 @ SV41 )
= $false )
| ( ( SV22 @ SV95 @ SV87 )
= $false )
| ( ( in @ SV87 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(559,plain,
! [SV41: $i,SV88: $i,SV22: $i > $i > $o] :
( ( ( SV22 @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV88 )
= $true )
| ( ( in @ SV88 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(560,plain,
! [SV22: $i > $i > $o,SV41: $i,SV88: $i] :
( ( ( in @ ( sK7_Xy @ SV88 @ SV41 @ SV22 ) @ SV41 )
= $true )
| ( ( in @ SV88 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( in @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(561,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(562,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i] :
( ( ( ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(563,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ~ ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) ) )
= $false )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(564,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i] :
( ( ( ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) )
= $false )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(565,plain,
! [SV89: $i,SV67: $i,SV23: $i] :
( ( ( ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(566,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(567,plain,
! [SV96: $i,SV67: $i,SV23: $i] :
( ( ( ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(568,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(569,plain,
! [SV23: $i,SV83: $i,SV78: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV78 )
| ( in @ SV104 @ SV83 ) )
= $true )
| ( ( ! [SY398: $i] :
( ~ ( in @ SY398 @ SV83 )
| ( in @ SY398 @ SV78 ) ) )
= $true )
| ( ( in @ SV78 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ SV83 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(570,plain,
! [SV23: $i,SV90: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV90 ) )
= $true )
| ( ( in @ SV102 @ SV23 )
= $true )
| ( ( in @ SV90 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(571,plain,
! [SV97: $i,SV23: $i,SV91: $i] :
( ( ( in @ SV91 @ SV23 )
= $false )
| ( ( ~ ( in @ SV97 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) ) )
| ( SV91 = SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(572,plain,
! [SV44: $i,SV30: $i,SV58: $i,SV101: $o] :
( ( SV101 = $false )
| ( SV101 = $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(573,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(574,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV58 = SV30 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(575,plain,
! [SV30: $i,SV98: $o,SV44: $i,SV58: $i] :
( ( ( in @ SV58 @ SV44 )
= $true )
| ( SV98 = $true )
| ( SV98 = $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(576,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( in @ SV58 @ SV44 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(577,plain,
! [SV30: $i,SV44: $i,SV58: $i] :
( ( ( in @ SV58 @ SV44 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(578,plain,
! [SV44: $i,SV30: $i,SV58: $i,SV99: $o] :
( ( ( ~ SV99 ) = $true )
| ( SV99 = $true )
| ( SV99 = $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(579,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(580,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(581,plain,
! [SV76: $i,SV41: $i,SV105: $i,SV22: $i > $i > $o] :
( ( ( ! [SY402: $i] :
( ~ ( SV22 @ SY402 @ SV105 )
| ~ ( in @ SY402 @ SV41 ) )
| ( in @ SV105 @ ( sK6_B @ SV41 @ SV22 ) ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(582,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV106 )
| ~ ( in @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV41 ) ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(583,plain,
! [SV76: $i,SV41: $i,SV22: $i > $i > $o] :
( ( ( ! [SY354: $i] :
( ! [SY355: $i] :
( ~ ( SV22 @ SY355 @ SY354 )
| ~ ( in @ SY355 @ SV41 ) )
| ( in @ SY354 @ ( sK6_B @ SV41 @ SV22 ) ) ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(584,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i] :
( ( ( ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SY356 )
| ~ ( in @ ( sK7_Xy @ SY356 @ SV41 @ SV22 ) @ SV41 ) ) ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(585,plain,
! [SV89: $i,SV67: $i,SV23: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ ( sK11_B @ SV23 ) )
| ! [SY403: $i] :
( ~ ( in @ SY403 @ SV107 )
| ( in @ SY403 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV107 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(586,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(587,plain,
! [SV96: $i,SV67: $i,SV23: $i] :
( ( ( ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK11_B @ SV23 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ SY384 )
| ( in @ SY385 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SY384 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(588,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(589,plain,
! [SV23: $i,SV83: $i,SV78: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV78 ) )
= $true )
| ( ( in @ SV104 @ SV83 )
= $true )
| ( ( ! [SY398: $i] :
( ~ ( in @ SY398 @ SV83 )
| ( in @ SY398 @ SV78 ) ) )
= $true )
| ( ( in @ SV78 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ SV83 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(590,plain,
! [SV23: $i,SV90: $i,SV102: $i] :
( ( ( in @ SV102 @ SV90 )
= $false )
| ( ( in @ SV102 @ SV23 )
= $true )
| ( ( in @ SV90 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(591,plain,
! [SV91: $i,SV23: $i,SV97: $i] :
( ( ( in @ SV97 @ SV23 )
= $false )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) ) )
| ( SV91 = SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(592,plain,
! [SV44: $i,SV30: $i,SV58: $i,SV99: $o] :
( ( SV99 = $false )
| ( SV99 = $true )
| ( SV99 = $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(593,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(594,plain,
! [SV44: $i,SV30: $i,SV58: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV58 @ ( setadjoin @ SV30 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(595,plain,
! [SV76: $i,SV41: $i,SV105: $i,SV22: $i > $i > $o] :
( ( ( ! [SY402: $i] :
( ~ ( SV22 @ SY402 @ SV105 )
| ~ ( in @ SY402 @ SV41 ) ) )
= $true )
| ( ( in @ SV105 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(596,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ ( sK6_B @ SV41 @ SV22 ) ) )
= $true )
| ( ( ~ ( ~ ( SV22 @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV106 )
| ~ ( in @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV41 ) ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(597,plain,
! [SV76: $i,SV41: $i,SV108: $i,SV22: $i > $i > $o] :
( ( ( ! [SY404: $i] :
( ~ ( SV22 @ SY404 @ SV108 )
| ~ ( in @ SY404 @ SV41 ) )
| ( in @ SV108 @ ( sK6_B @ SV41 @ SV22 ) ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(598,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV109: $i] :
( ( ( ~ ( in @ SV109 @ ( sK6_B @ SV41 @ SV22 ) )
| ~ ( ~ ( SV22 @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV109 )
| ~ ( in @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV41 ) ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(599,plain,
! [SV89: $i,SV67: $i,SV23: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ ( sK11_B @ SV23 ) ) )
= $true )
| ( ( ! [SY403: $i] :
( ~ ( in @ SY403 @ SV107 )
| ( in @ SY403 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV107 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(600,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(601,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(602,plain,
! [SV96: $i,SV67: $i,SV23: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ ( sK11_B @ SV23 ) )
| ! [SY405: $i] :
( ~ ( in @ SY405 @ SV110 )
| ( in @ SY405 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV110 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(603,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(604,plain,
! [SV23: $i,SV83: $i,SV78: $i,SV104: $i] :
( ( ( in @ SV104 @ SV78 )
= $false )
| ( ( in @ SV104 @ SV83 )
= $true )
| ( ( ! [SY398: $i] :
( ~ ( in @ SY398 @ SV83 )
| ( in @ SY398 @ SV78 ) ) )
= $true )
| ( ( in @ SV78 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ SV83 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(605,plain,
! [SV23: $i,SV91: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) ) ) )
= $true )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(606,plain,
! [SV76: $i,SV41: $i,SV105: $i,SV111: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ SV111 @ SV105 )
| ~ ( in @ SV111 @ SV41 ) )
= $true )
| ( ( in @ SV105 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(607,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV106: $i] :
( ( ( in @ SV106 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( ~ ( ~ ( SV22 @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV106 )
| ~ ( in @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV41 ) ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(608,plain,
! [SV76: $i,SV41: $i,SV108: $i,SV22: $i > $i > $o] :
( ( ( ! [SY404: $i] :
( ~ ( SV22 @ SY404 @ SV108 )
| ~ ( in @ SY404 @ SV41 ) ) )
= $true )
| ( ( in @ SV108 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(609,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV109: $i] :
( ( ( ~ ( in @ SV109 @ ( sK6_B @ SV41 @ SV22 ) ) )
= $true )
| ( ( ~ ( ~ ( SV22 @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV109 )
| ~ ( in @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV41 ) ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(610,plain,
! [SV89: $i,SV67: $i,SV23: $i,SV107: $i] :
( ( ( in @ SV107 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( ! [SY403: $i] :
( ~ ( in @ SY403 @ SV107 )
| ( in @ SY403 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV107 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(611,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(612,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(613,plain,
! [SV96: $i,SV67: $i,SV23: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ ( sK11_B @ SV23 ) ) )
= $true )
| ( ( ! [SY405: $i] :
( ~ ( in @ SY405 @ SV110 )
| ( in @ SY405 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV110 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(614,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(615,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(616,plain,
! [SV23: $i,SV104: $i,SV78: $i,SV83: $i,SV112: $i] :
( ( ( ~ ( in @ SV112 @ SV83 )
| ( in @ SV112 @ SV78 ) )
= $true )
| ( ( in @ SV104 @ SV83 )
= $true )
| ( ( in @ SV104 @ SV78 )
= $false )
| ( ( in @ SV78 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ SV83 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(617,plain,
! [SV23: $i,SV91: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) ) )
= $false )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(618,plain,
! [SV76: $i,SV41: $i,SV105: $i,SV111: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ SV111 @ SV105 ) )
= $true )
| ( ( ~ ( in @ SV111 @ SV41 ) )
= $true )
| ( ( in @ SV105 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(619,plain,
! [SV76: $i,SV41: $i,SV106: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV106 )
| ~ ( in @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV41 ) )
= $false )
| ( ( in @ SV106 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(620,plain,
! [SV76: $i,SV41: $i,SV108: $i,SV113: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ SV113 @ SV108 )
| ~ ( in @ SV113 @ SV41 ) )
= $true )
| ( ( in @ SV108 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(621,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV109: $i] :
( ( ( in @ SV109 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( ~ ( ~ ( SV22 @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV109 )
| ~ ( in @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV41 ) ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(622,plain,
! [SV89: $i,SV23: $i,SV67: $i,SV107: $i] :
( ( ( ! [SY403: $i] :
( ~ ( in @ SY403 @ SV107 )
| ( in @ SY403 @ ( sK13_SY253 @ SV67 @ SV23 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV107 )
= $true )
| ( ( in @ SV107 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(623,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(624,plain,
! [SV89: $i,SV23: $i,SV67: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SV114 @ SV67 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(625,plain,
! [SV96: $i,SV67: $i,SV23: $i,SV110: $i] :
( ( ( in @ SV110 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( ! [SY405: $i] :
( ~ ( in @ SY405 @ SV110 )
| ( in @ SY405 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
| ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV110 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(626,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(627,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ! [SY386: $i] :
( ~ ( in @ SY386 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SY386 @ SV67 ) ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(628,plain,
! [SV23: $i,SV104: $i,SV78: $i,SV83: $i,SV112: $i] :
( ( ( ~ ( in @ SV112 @ SV83 ) )
= $true )
| ( ( in @ SV112 @ SV78 )
= $true )
| ( ( in @ SV104 @ SV83 )
= $true )
| ( ( in @ SV104 @ SV78 )
= $false )
| ( ( in @ SV78 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ SV83 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(629,plain,
! [SV23: $i,SV91: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) ) )
= $false )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(630,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) ) )
= $false )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(631,plain,
! [SV76: $i,SV41: $i,SV105: $i,SV111: $i,SV22: $i > $i > $o] :
( ( ( SV22 @ SV111 @ SV105 )
= $false )
| ( ( ~ ( in @ SV111 @ SV41 ) )
= $true )
| ( ( in @ SV105 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(632,plain,
! [SV76: $i,SV41: $i,SV106: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV106 ) )
= $false )
| ( ( in @ SV106 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(633,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV106: $i] :
( ( ( ~ ( in @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV41 ) )
= $false )
| ( ( in @ SV106 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(634,plain,
! [SV76: $i,SV41: $i,SV108: $i,SV113: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ SV113 @ SV108 ) )
= $true )
| ( ( ~ ( in @ SV113 @ SV41 ) )
= $true )
| ( ( in @ SV108 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(635,plain,
! [SV76: $i,SV41: $i,SV109: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV109 )
| ~ ( in @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV41 ) )
= $false )
| ( ( in @ SV109 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(636,plain,
! [SV89: $i,SV23: $i,SV67: $i,SV107: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV107 )
| ( in @ SV115 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
= $true )
| ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV107 )
= $true )
| ( ( in @ SV107 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(637,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(638,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(639,plain,
! [SV89: $i,SV23: $i,SV67: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ SV114 @ SV67 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(640,plain,
! [SV96: $i,SV23: $i,SV67: $i,SV110: $i] :
( ( ( ! [SY405: $i] :
( ~ ( in @ SY405 @ SV110 )
| ( in @ SY405 @ ( sK13_SY253 @ SV67 @ SV23 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV110 )
= $true )
| ( ( in @ SV110 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(641,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
| ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(642,plain,
! [SV96: $i,SV23: $i,SV67: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ ( sK13_SY253 @ SV67 @ SV23 ) )
| ~ ( in @ SV116 @ SV67 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(643,plain,
! [SV23: $i,SV104: $i,SV78: $i,SV83: $i,SV112: $i] :
( ( ( in @ SV112 @ SV83 )
= $false )
| ( ( in @ SV112 @ SV78 )
= $true )
| ( ( in @ SV104 @ SV83 )
= $true )
| ( ( in @ SV104 @ SV78 )
= $false )
| ( ( in @ SV78 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ SV83 @ ( sK11_B @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(644,plain,
! [SV23: $i,SV91: $i,SV97: $i] :
( ( ( in @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) @ ( sK11_B @ SV23 ) )
= $true )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(645,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) ) )
= $true )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(646,plain,
! [SV76: $i,SV105: $i,SV22: $i > $i > $o,SV41: $i,SV111: $i] :
( ( ( in @ SV111 @ SV41 )
= $false )
| ( ( SV22 @ SV111 @ SV105 )
= $false )
| ( ( in @ SV105 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(647,plain,
! [SV76: $i,SV41: $i,SV106: $i,SV22: $i > $i > $o] :
( ( ( SV22 @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV106 )
= $true )
| ( ( in @ SV106 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(648,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV106: $i] :
( ( ( in @ ( sK7_Xy @ SV106 @ SV41 @ SV22 ) @ SV41 )
= $true )
| ( ( in @ SV106 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $true )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(649,plain,
! [SV76: $i,SV41: $i,SV108: $i,SV113: $i,SV22: $i > $i > $o] :
( ( ( SV22 @ SV113 @ SV108 )
= $false )
| ( ( ~ ( in @ SV113 @ SV41 ) )
= $true )
| ( ( in @ SV108 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(650,plain,
! [SV76: $i,SV41: $i,SV109: $i,SV22: $i > $i > $o] :
( ( ( ~ ( SV22 @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV109 ) )
= $false )
| ( ( in @ SV109 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(651,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV109: $i] :
( ( ( ~ ( in @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV41 ) )
= $false )
| ( ( in @ SV109 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(652,plain,
! [SV89: $i,SV23: $i,SV67: $i,SV107: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV107 ) )
= $true )
| ( ( in @ SV115 @ ( sK13_SY253 @ SV67 @ SV23 ) )
= $true )
| ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV107 )
= $true )
| ( ( in @ SV107 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(653,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(654,plain,
! [SV89: $i,SV23: $i,SV67: $i] :
( ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[638]) ).
thf(655,plain,
! [SV89: $i,SV23: $i,SV67: $i,SV114: $i] :
( ( ( in @ SV114 @ ( sK13_SY253 @ SV67 @ SV23 ) )
= $false )
| ( ( ~ ( in @ SV114 @ SV67 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(656,plain,
! [SV96: $i,SV23: $i,SV67: $i,SV110: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV110 )
| ( in @ SV117 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
= $true )
| ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV110 )
= $true )
| ( ( in @ SV110 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(657,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(658,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(659,plain,
! [SV96: $i,SV23: $i,SV67: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ ( sK13_SY253 @ SV67 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ SV116 @ SV67 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(660,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
| ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) )
= $false )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(661,plain,
! [SV76: $i,SV108: $i,SV22: $i > $i > $o,SV41: $i,SV113: $i] :
( ( ( in @ SV113 @ SV41 )
= $false )
| ( ( SV22 @ SV113 @ SV108 )
= $false )
| ( ( in @ SV108 @ ( sK6_B @ SV41 @ SV22 ) )
= $true )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(662,plain,
! [SV76: $i,SV41: $i,SV109: $i,SV22: $i > $i > $o] :
( ( ( SV22 @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV109 )
= $true )
| ( ( in @ SV109 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(663,plain,
! [SV76: $i,SV22: $i > $i > $o,SV41: $i,SV109: $i] :
( ( ( in @ ( sK7_Xy @ SV109 @ SV41 @ SV22 ) @ SV41 )
= $true )
| ( ( in @ SV109 @ ( sK6_B @ SV41 @ SV22 ) )
= $false )
| ( ( SV76
= ( sK9_SY248 @ SV76 @ SV41 @ SV22 ) )
= $false )
| ( ( SV22 @ ( sK8_SY20 @ SV41 @ SV22 ) @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(664,plain,
! [SV89: $i,SV23: $i,SV67: $i,SV107: $i,SV115: $i] :
( ( ( in @ SV115 @ SV107 )
= $false )
| ( ( in @ SV115 @ ( sK13_SY253 @ SV67 @ SV23 ) )
= $true )
| ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV107 )
= $true )
| ( ( in @ SV107 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(665,plain,
! [SV89: $i,SV23: $i,SV67: $i,SV114: $i] :
( ( ( in @ SV114 @ SV67 )
= $false )
| ( ( in @ SV114 @ ( sK13_SY253 @ SV67 @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ SV89 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(666,plain,
! [SV96: $i,SV23: $i,SV67: $i,SV110: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV110 ) )
= $true )
| ( ( in @ SV117 @ ( sK13_SY253 @ SV67 @ SV23 ) )
= $true )
| ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV110 )
= $true )
| ( ( in @ SV110 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(667,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( in @ ( sK13_SY253 @ SV67 @ SV23 ) @ ( sK11_B @ SV23 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(668,plain,
! [SV96: $i,SV23: $i,SV67: $i] :
( ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV67 )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[658]) ).
thf(669,plain,
! [SV96: $i,SV23: $i,SV67: $i,SV116: $i] :
( ( ( in @ SV116 @ ( sK13_SY253 @ SV67 @ SV23 ) )
= $false )
| ( ( ~ ( in @ SV116 @ SV67 ) )
= $true )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(670,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( ~ ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) )
= $false )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(671,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( ~ ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) ) )
= $false )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(672,plain,
! [SV96: $i,SV23: $i,SV67: $i,SV110: $i,SV117: $i] :
( ( ( in @ SV117 @ SV110 )
= $false )
| ( ( in @ SV117 @ ( sK13_SY253 @ SV67 @ SV23 ) )
= $true )
| ( ( in @ ( sK14_SY267 @ SV67 @ SV23 ) @ SV110 )
= $true )
| ( ( in @ SV110 @ ( sK11_B @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(673,plain,
! [SV96: $i,SV23: $i,SV67: $i,SV116: $i] :
( ( ( in @ SV116 @ SV67 )
= $false )
| ( ( in @ SV116 @ ( sK13_SY253 @ SV67 @ SV23 ) )
= $false )
| ( ( in @ ( sK15_Xx @ SV67 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ SV96 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(674,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
= $true )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(675,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
| ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
= $true )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(676,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
= $true )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(677,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
= $true )
| ( ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
= $true )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(678,plain,
! [SV23: $i,SV97: $i,SV91: $i] :
( ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
= $false )
| ( ( ~ ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) ) )
= $true )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(679,plain,
! [SV23: $i,SV91: $i,SV97: $i] :
( ( ( in @ SV97 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
= $false )
| ( ( in @ SV91 @ ( sK12_SY266 @ SV97 @ SV91 @ SV23 ) )
= $false )
| ( ( SV91 = SV97 )
= $true )
| ( ( in @ SV91 @ SV23 )
= $false )
| ( ( in @ SV97 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(680,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[78,679,677,673,672,668,667,665,664,663,662,661,654,653,648,647,646,644,643,594,593,592,590,577,576,575,574,573,572,560,559,558,557,547,546,545,531,520,519,488,485,480,477,476,475,463,460,459,458,457,456,455,454,431,430,426,423,419,410,409,408,386,374,361,349,345,341,329,308,294,267,266,264,263,238,237,236,235,234,233,208,179,170,169,168,167,166,163,145,125,124,102]) ).
thf(681,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[680]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU520^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n008.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:28:09 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.59/0.47
% 1.59/0.47 No.of.Axioms: 0
% 1.59/0.47
% 1.59/0.47 Length.of.Defs: 8001
% 1.59/0.47
% 1.59/0.47 Contains.Choice.Funs: true
% 1.59/0.47 ...........................
% 1.59/0.47
% 1.59/0.47 ********************************
% 1.59/0.47 * All subproblems solved! *
% 1.59/0.47 ********************************
% 1.59/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:36,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:680,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.59/0.47
% 1.59/0.47 %**** Beginning of derivation protocol ****
% 1.59/0.47 % SZS output start CNFRefutation
% See solution above
% 1.59/0.48
% 1.59/0.48 %**** End of derivation protocol ****
% 1.59/0.48 %**** no. of clauses in derivation: 681 ****
% 1.59/0.48 %**** clause counter: 680 ****
% 1.59/0.48
% 1.59/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:36,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:680,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------